I'm so sorry.
2) Right when Bruce Wayne (the wealthiest person in Gotham) comes back, Batman starts shortly after
Right when Bruce Wayne becomes a recluse (after TDK), Batman is also a recluse
3) Right after Bruce Wayne attends a public charity event (with the town talking about it), Batman comes back
2. I don't think BB really establishes how long that preparation montage really took in real life, though. What if it was half a year or something?
Bruce Wayne only becomes a recluse after that clean energy project fails, while Batman I believe really hadn't made an appearence since then. (And even if he did, shouldn't have been at the same time regardless)
3. Yeah
For all the "realism" these movies have "grounded" their story in, the plot and general storytelling style still heavilty run on magical thinking / daydream fulfillment - so they just don't give all too much thought to stuff like that. The way Bruce/Batman emerge roughly at the same time just fits the rhythm of the movie, and the way the viewer is rooting for Bruce to return and start making changes - what the world thinks of it, why they don't just put 2 and 2 together, seems to be of secondary importance at best.
I'm not even sure if that's a "bad" thing really - these movies are still fast and loose escapist entertainment mostly focused on tone and emotions, so maybe those breaks from reality ultimately just really serve the tone the movies were going for? Maybe at some point in the future, someone will decide to make an ultra-realistic Batman movie, really trying to make it as believable as possible, and then it turns out to be really awesome - but these Nolan movies are still, to a considerable degree, fantastical in nature.
However, I'm by no means saying that this excuses EVERY plot hole in these movies, and the third one is really the one where these problems begin to compound on the movie to a palpable degree, and it starts showing cracks.
It doesn't really help that while BB had its "simplistic origin story" tone to fall back on, and TDK was this nightmarish descent into madness that hardly left the viewer a break in the midst its breathless pace, this last one really kinda shines a giant spotlight on its own problems by presenting itself as the "be-all end-all epic conclusion of the saga wrapping everything together" that it kinda is. Yea, your wrap-up at the Italian coffeehouse there kinda feels like a surreal daydream, as does the rest of the movie - was that really the intention? I kinda doubt it.
Case in point:
To me most of us and most of Gotham should have too. What's unbelievable is how nobody else figures it out. NOT that Blake did.
"Even in TDKR though, there was no point where a civilian or officer would take a close-up picture of Batman's face. [...]"
Really? Surrounded by cops, lights and helicopter, no one could have taken any kind of footage? What about street cameras? Geez, you really underestimate today´s technology and the police force. And you really have to, in order to believe Batman could actually exist.
Yes, you see, when the first movie came on the scene, it established certain rules of suspension of disbelief that were easy to follow - just like Superman and his glasses (and, admittedly, pretty ****ing masterful changes in body language and facial expression), you just kinda accept that in this made-up world, no one recognizes a person based on his jawline; you roll with it just like you might roll with theatrical conventions such as masks or "surreptitious winks" when watching certain kinds of plays, and still take the rest more or less at face value.
Because really, why does he show off a half of his face? To be able to make an angry fury face at Flass? Fine, but that might also kinda defeat the whole "is he really a human" angle that seemed so successful at instilling at least irrational fear in his victims. The movie's not clear on it, but either interpretation - that the people here have inferior facial recognition skills, or that he's "really" wearing a mask over his whole face, or maybe with some black war paint all over it (that fear toxin version sure looked loads scarier than the actual one), and only looks the way he does "to the audience" for stylistic purposes - can just be accepted for the rest of the flick without creating any problems otherwise.
The people not making the sort of connections pointed out above? Established, let's move on - so maybe they're all distracted, or there's lots of billionaires travelling about all the time. Who cares - it does pull the movie a bit away from realistic towards the make-believe, but you just roll with it and move on: they don't make the connection, and that's it really.
The problems only really start when the story begins to BREAK its own rules. Like Lois suddenly noticing that Clark kinda looks like Superman in Superman II... yeah, really? Or in this case, some employee just finding a whole open archive containing all of Batman's well-kept secrets, and one special orphan recognizing more than just a scarred orphan in a particularly rich orphan.
Things fall apart - get surreal. They make you question the conventions you'd just been swallowing all this time without wasting much thought on it, shine a giant light on their questionability, and, well, a “flaw” emerges.
So now maybe you see how your whole point about everyone else not figuring it out like these two being the real problem, rather than these two figuring it out being the problem,
is the true problem - it WASN'T a problem before the story committed the
mistake of breaking its own rules, and
made it into one. It's kind of almost like that bit in the Neverending Story novel - a minute ago the desert didn't exist, but now it does, and has been existing for eons; a moment ago, Batman's indetectability was a given.. now it's been a giant plot hole all along.
And if instead you cling to the previously established rule due to how engagingly it was presented, well, then Reese and Blake seem absurd (Blake either way

)! No matter which angle you choose to look at it from, the picture no longer fits together.
(The answer to your question why the cops didn't take a picture?
If this were the real Batman, or a truly realistic movie this kind of scrutiny actually wouldn't be wasted on, he would be concealing his whole face (unless he already does it

), and there would be (=is) nothing to take.
Hey, why didn't Bruce come up with a better escape plan than just turn off the lights and fly into a giant open cave near the freeway? What if some helicopters shone a spotlight on him? Cause it's the Batmobile, and he's just brilliant and slippery like that - end of story. Good enough for this movie

)
So, Coleman Reese… he’s not that great. Doesn’t make too much sense if you really look at it.
While the specifics of how Wayne and his triumvirate managed to keep their project a complete secret, ordering small but still fairly… recognizeable components from different companies and whatnot, certainly can be called into question when it comes to their plausibility – what matters is that in the movie’s plot, they *worked*.
And were probably bound to work from the beginning, given how, right after Alfred scrapped his plans to call the shrinks, he and Bruce must have sat down and discussed the feasibility of such a project – and arrived at the conclusion that, yes, it was pretty much feasible, before actually starting to work on all the equipment.
Well, at least the equipment that hadn’t already been produced long time ago, but surely the two have covered all the risks of someone exposing those connections before deciding to include the tumbler in their arsenal – and if there were any holes left that, say, only Fox could take care of, well, Fox sure must’ve covered those up after joining the team. If it weren’t for that, the secret wouldn’t be safe – and given how they decided to use it, and remained super confident about its secrecy the whole time after that, it obviously was.
So, all of a sudden, some guy comes along and cracks said reliably hidden secret…
Oops! What just happened?
Apparently, the blueprints are still available after all – and not just anywhere, but in a place a fiduciary working for the company easily had access to! Fox, having apparently done nothing to close this giant security leak, doesn’t have any qualms whatsoever about ordering said fiduciary to do exactly the kinds of research that would lead him to places where he could find the blueprints, or UNNECESSARILY TELLING HIM TO DO SAID RESEARCH AGAIN. Wow, certainly testing the odds there isn’t he… but no worries, if someone should (likely) find out about it, he still can threaten them with Batman and all is well, right! Well… why exactly? Yea, Reese doesn’t do anything to disprove his assumption that he won’t just go tell the police (or the mob for that matter) – but he totally could, because with Fox/Wayne arrested/under surveillance/killed, there wouldn’t be any possibility for Wayne OR Batman to come after him. Oops!
What, he won’t because Enterprises pays him well, even without the blackmail? Yea, let’s just bet on that and go back to reading the paper with a smile of smug self-satisfaction. He and the rest of the triumvirate will remain as unworried and confident about the safety of their secret as they’ve been the entire time before this incident until Reese unexpectedly decides to spill the beans anyway – and once he doesn’t, forget about it again.
So no, nothing is alright with the Reese subplot - the ease with which he's able to stumble upon the secret (and with that, the question why no one else has so far), as well as Fox’ frivolous attitude toward this incredibly serious problem, does srs harm to that scene’s believability, almost to the point of making it appear completely farcical.
However, the way it’s written and acted is quite entertaining in itself, and it also obviously serves its role as a chess piece in the rather delicious web of set-ups and pay-offs that is that movie’s plot – and with the frantic, driving pace and atmosphere of this movie doing its best to distract and engage the viewer, one is easily seduced to simply appreciate this scene for how inconspicuously and “elegantly” it sets up a completely awesome plotline later in the film, instead of despairing of its complete and utter lack of sense.
That and, as another user has already pointed out, if you take this scene as an intentional, (not-so-)subtle jab at the series’ own logic, that certainly can’t hurt your enjoyment/appreciation of it. Might make you frown a bit at the movie for breaking its believability like this, but still take it with a grain of sugar.
That last one, of course, in no way applies to its TDKR’s counterpart – there isn’t a shred of self-irony in that one; it’s played completely straight.
The tone of that scene is dramatic, serious, and of course totally emotional – a much frailer shield against merciless scrutiny than irony and humour. But… still one that often works, and that’s why I really can’t hold it in the same contempt as many others here.
No, it doesn’t really make sense, and yes, you can make up a bunch of fill-in-the-blanks-off-screen-**** to explain it away but that’s technically apologetics isn’t it?
But it can work as a vicarious wish fulfilment and that way appeal to the emotional side of the viewer – causing them to ignore, or even appreciate its lack of logic. See, Bruce can’t share his secret with anyone and puts on a mask all the time – he has to, the secret can’t get out by any means, and yet it’s entirely possible that some part of him (and/or, vicariously, the viewer’s) has a desire for someone, preferably someone he can relate to, someone upright and admirable rather than a bullsh** jerk, to just see through the mask and recognize his true self, breaking the ice to speak. Same with Blake - he “recognizes” his idol in someone he can relate to, *by* relating to him, and now starts “mattering” to said idol and their common ideals by telling him he knows and understands.
There’s the relief aspect, finding someone you can relate and talk to, a bit of mentor/apprentice fantasy (no, not that one), the general w&f appeal of meaningful coincidences and ambiguous “psychic connections”, and all delivered with convincing acting and a slightly dream-like atmosphere – enough to get a viewer “hooked”. And once they’re hooked, that’s where their brains can start making excuses and filling in the blanks, not to “justify” it as a competent, thought-out creator decision, but simply, provided there’s a need for that in the first place, in order to buy what’s happening more easily.
Subtext (Blake really meaning that he’s done some research/observation based on that initial hunch, but finding no need to spell it out / trying to grab Bruce emotionally at first), slight dishonesty (saying he knew already back then, but actually just having confirmed his growing suspicions when Alfred let him in), off-screen dialogue (Blake proceeds to explain the rest to him in the car), you name it – anything that COULD’VE happened behind the scenes, or between the lines, and thus elevated this plot point to a level of possibility/plausibility. And when there’s a desire to buy something, that’s often all it takes.
(Oh, but seriously **** the question which of the kids came up with “Batman” in its brown buttocks – who cares?! Once you’re in the game of making up “stories” and “legends” about one particular person, Batman is one of the very few masked celebrities in town and can't really be that far from the top of the list either way; guessing who Batman is, much more difficult, but the other way around? Gimme a fking break – Blake came up with it, other kids came up with it and that gave him the needed hunch, the point is once that idea sat there in head he immediately realized its veracity, and for that he had no frggin reason)
But when returning to the discussion about whether “Nolan” was “justified” to just put it in there, not dropping a single word about anything that could possibly remove the sheer absurdity from Blake’s story as taken at face value, or, God forbid, whether it is actually absurd when taken at face value (yes it is), obviously that kind of reasoning isn’t really valid – because who’s to say the authors gave it anywhere this much thought, if there’s really no evidence for that in the movie?
Me personally, I kinda saw both sides – saw the emotional appeal, from a bit of a distance I guess, but was also thrown off by how little sense it made. Watching the movie with my monkey brain though, as usual, I really just took it for what it essentially was – a fairly engaging scene that establishes a character relationship / introduces Blake to the “in-the-know protagonist team” and influences the plot in the way it does – and just went along with the flow; the movie hadn’t thrown me off the rails yet (that came laturr – when Alfred left) and felt, well, fairly engaging so far, so I just swallowed it and didn’t mind.
The thing, to come back to it once more, and largely also the problem with TDKR is that it’s generally further removed from “realism” (i.e. a realistic way in which events unfold, characters act etc.) than the two previous ones – and while those were still believable enough to “buy into”, the first as a real-feeling heroic tale and the second as an even more real-feeling world devolving into somewhat of a nightmare (which just might be the way the characters in it feel like), this one has several scenes in it where it really starts to slip and feeling more like a dream/fantasy than a realistic story.
It starts right at the beginning, with the rather unexpected time leap – that takes place DURING THE OPENING SCENE! A “flashback” to Gordon’s TDK speech, followed by the Bane scene – in the story, a new threat that comes to haunt the now established peace with Gordon’s lie as a background, hence the flashback, but when watching the movie? By opening with a TDK shot, the movie just reinforces the viewer’s assumption that Gotham is roughly in the state you expect it to be based on how that movie ended, and keeps up that assumption for entire 5 minutes before, oops, I guess things are completely different now! So… Bane’s not coming to fuel the mob / Joker chaos, then?
This, and the questionable nature of those developments (especially Bruce’s retirement), make it feel off, weird, like it’s taking place in some alternate reality or something. Yea… all the mafia is gone, isn’t that wonderful? Sounds a bit too good to be true? Then Gordon starts speaking, and the scene has that kind of dream-like atmosphere to it, just like that fade-in fade-out flashback from 5 minutes ago, and it’s done – the movie’s gotten up on the wrong side of the bed (if it’s gotten up at all… Inception!!1!).
But then we kind of start get used to this new world, the characters discuss some of the backstory and it all seems to make sense in the end – looks like the movie’s getting back on trac- ohhhhh wait the new cop’s here and he knows who Bruce is. Yeaaahh… it’s just his fever dream isn’t it.
After that, weird things keep piling up – Alfred gets completely out-of-character, as does Bruce, they have an inexplicable fall-out (notice the dream-like I mean emotional lighting in that scene); then our hero suddenly gets to play with two new fantasy girlfriends, one of whom he starts impressing with his two alter egos and somehow inexplicably gets away with it (so much for the “Blake couldn’t have seen a close-up photograph” argument huh), and the other just suddenly sleeps with him after suddenly stopping by his house.
Some Like it Hot meets Alone in the Dark?
Some strange “clean-slate device” that everyone talks about, and Bruce Wayne somehow “has”… don’t explain anything, he just does. His subconscious dreams it up, and he then just fills it with… wait, no.
Something that looks like the well he fell in as a kid, and somehow has bats in it even though there haven’t been any bats around since the first movie… well, the whole prison and revolution threads actually feel very tangible, I can totally buy all the stuff that goes on in Gotham etc., but then Alfred has his surreal café thing, the rookie becomes the new Batman, and you finally understand what’s going on here – Batman came back home that night, exhausted, and burdened by this new conspiracy he’s now part of, plunged down on his decadent billionaire couch and fell into a deep, deeper sleep in front of some damn good TV.
What happens when he wakes up? Hopefully a much better movie.
So, in conclusion, you can really make of Blake what you will – yes, it’s nonsensical and surreal, but then the whole movie is a bit like that, so does that make it fit in with the rest? Or should this “rest” have never been there in the first place, as it drags down the movie and probably wasn’t really intended to end up this way either?
I’m more in the latter camp here – each time some of that weird **** appears on the screen, the movie goes to die. All I wanted to see was Bane and his revolution. and some much, much better cartilage filling up the rest than what ended up in the movie; much like like DK

That one, you could theoretically watch all Joker scenes on youtube (edited together as they tend to be), and then, curious how it’s all connected together, watch the whole movie, and be blown away by all the tense stuff that happens inbetween, how tight the structure is and how well it balances its trump card with all the rest. The way it mfking builds up to the party crash… omg.
Here, you’ve got Bane giving an awesome captivating speech and you’re totally into it, and then it keeps cutting to Gordon and Levitt having an awkward joke of an argument in front of the TV. MEH.