Just got back from the film for the second time. I stand by my 8.5/10. It's a very good film.
I think a lot of the problems some people have with it, is really just not paying attention. I've heard people on here say things like, "The Parademons looked cool. The one that crashes out of Martha Wayne's grave was terrifying." This is a small example, but that was not a Parademon (those were in the Knightmare sequence only) this was a giant bat. If these are details fans are missing, I don't know what to say other than pay a little better attention. I've heard reviewers complain about "a dirty bomb plot that goes no where." SERIOUSLY? Just watch the film.
As for what people think was convoluted or didn't add up, let's go point-by-point:
Bruce Wayne/Batman's motivations:
He is present for the Black Zero event in Metropolis. He saves who he can and sees the damage that this new era of Gods can do. He is paranoid and afraid of what this means for the human race.
Cut to 18 months later and he has been tracking a weapon, a mineral, that can kill a Kryptonian. He is tracking the Russians (who are smuggling the weapon). He lies to Alfred and tells him that he is tracking a dirty bomb because he knows Alfred will not agree with him starting a pre-emptive war with Superman.
Bruce is blinded by paranoia of an enemy he knows the world would not be able to defeat. An enemy that has struck him at his core when it killed hundreds of his employees during the Black Zero event. He is pushed even further when he sees the effect that the event had on one of his workers, Wallace Keefe. The letters scribbled on the survivor's checks that Keefe has been sending back to Wayne Enterprises goad Wayne on more (Wayne doesn't know that these checks have actually been intercepted by Luthor and it is Lex who is returning them to Wayne Enterprises with the hateful messages). The incident at the Capitol is the final straw. It doesn't matter to Bruce if Superman caused the explosion. Because in any event, he did cause it. He caused Keefe's injuries and drove him to the point of becoming a martyr. And he is SUPERMAN and was there and did nothing to stop it.
Bruce clones Anatoli Knyazev/KGBeast/the lead Russian merc's phone and discovers that the Russians are in constant communication with Lex Luthor. After breaking into Luthor's server room while a guest at a party, Bruce gets all the information that Lex has on metahumans as well as "Kryptonite" and its uses.
He uses this information to create weapons (a spear and gas grenades) to take out Superman.
Superman issues Batman a warning not to go to the bat-signal if it is ever lit again. So to summon Superman, Batman lights the bat-signal and waits for Superman to arrive.
Lex Luthor's motivations/plan:
Lex Luthor hates Superman. This isn't just because in every iteration Lex hates Superman. It's because Lex is, in this film, one of (if not) the smartest person in the world. And as he points out, his knowledge should be true power. Power that is greater than someone like Superman's. Lex also fears the power of the Man of Steel and what he could do the world if he were to ever go rogue. Lex believes that it should be a MAN who is the savior of mankind, not an alien. His fears and hatred of all things inhuman has led to him studying and tracking all possible people with powers. He believes that all of our modern myths are based on actual people with incredible power: the "metahuman thesis." He looks for contingencies to take each possible metahuman out -- starting with Superman.
He knows about Batman. Batman has been around for 20 years and has no doubt made a reputation for being the most capable man (physically) in the world. Someone who could dispose of Superman if given the proper motivation and tools.
So Lex hammers home the motivation for Bruce. He sends him the letters from Wallace Keefe. He sets in motion the events in Africa to frame Superman and sully his reputation and causes the explosion at the Capitol. Lex provides the tool by allowing Batman to steal the Kryptonite (there is a smirk on his face as he sees the batarang in the glass case where the Kryptonite should be).
He kidnaps Martha Kent to use as leverage on Superman and kidnaps Lois Lane to bring Superman to him.
His plan is simple: Expose Superman as a fraud, or have him killed.
Option A: Superman flies to Gotham and kills the Batman. He brings Batman's head to Luthor at the site of the crashed alien ship where there are hundreds of network news cameras and Luthor can show the world that Superman is the killer everyone thought he is and ruin his reputation for good ...
... or ...
Option B: Batman uses the hate for Superman that Luthor has fueled and the weapons that Luthor has essentially supplied him with (Lex is the one who found and smuggled the Kryptonite from another hemisphere) to kill Superman. The end. Clean and simple.
Either option leaves Superman out of Luthor's way. Broken or dead. Those are Superman's two options as he flies to Gotham to confront Batman.
Doomsday:
Doomsday is Luthor's fail safe. He is what happens if Superman somehow escaped his catch 22 and was able to save Martha without killing Batman.
Lex believes that since Doomsday is "blood of my blood" that he can control him. His hubris is his downfall. As he says to Zod's corpse as he drips his blood onto his face, "Like Icarus you flew too close to the sun." This is exactly what Lex ultimately does. He believes that he can create a God to destroy Superman and that he will be able to control his creation. He is wrong. Very wrong.
Knightmare:
This was one of two things.
Option A: It was a dream that Bruce has based on his own paranoias.
Option B: It was a hard flash forward into an actual future in which Lois is dead or somehow out of the picture, and Superman has become a tyrant and blames Batman for her fate. Backed and corrupted by Darkseid, Superman rules over parts of the planet with his own Parademon-assisted army of followers.
Flash appears to tell Bruce that he needs to protect Lois and that Bruce was right about Superman all along. That Superman could destroy the world if he wanted to and that Bruce needs to find the other metahumans to stop the coming apocalypse. Of course, Bruce has no idea what Flash is talking about because Flash arrived too far into the past. Still, his appearance shakes Bruce and convinces him to find the other metahumans.
It has to be Option B, because Option A relies on Bruce having precognitive skills and premonitions that can see the actual future.
These issues seem to be some of people's biggest. All the information is presented in the film. They really aren't issues.
The only real leaps you need to make are how Lex Luthor knew that Bruce Wayne and Batman were the same person and that Clark Kent is Superman.
But when you consider that he is a driven madman with limitless resources, he could have poured all of them into discovering these truths prior to the film's start.
Well said 
