There would be no trouble seeing that it wasn't the doctor, but the main point is that they bothered to put a tiny amount of the doctor's blood into the body, showing that the writers have no clue about how you perform an autopsy.
It will be found out instantly given that they went about it using a terrorist attack, and Bruce Wayne can of course just say that he never authorized it. They couldn't have made it easier to find out.
My point is that all of them can't have been down there and even if there are still a few thousand that went down, which is still absurd (and possibly exaggerated given the shot we see of them), there would be somewhere around 40 000 officers left above ground, given the size of Gotham. Even without getting detailed, which you probably won't during the film, you still instinctively now that there would be tens of thousands of cops around. Yet when the cops underground get let out they can take on the well-armed terrorists in a fist fight.
And as said, I just posted four examples. There are many things like that going on in this film.
I'm just gonna say this. The TDK trilogy is not realistic, It never has been and it never made any claim that it was. Chris Nolan's intent was to create a world that vaguely resembled our own but operated on movie logic. His intent was never to create a movie series actually set in the real world. They have technology (the microwave emitter, the sonar device) you wouldn't find in the real world, An ancient ninja organization that caused the Great London Fire, they have plot points like Batman being able to kidnap a Chinese national with no international repercussions, and Harvey Dent being able to function with half his face burned off (how is that more "realistic" than police being able to fight terrorists after months underground)
That's why I don't find any of the examples of "ridiculous logic" you've laid out to hold any water. Regardless of whether or not it's more grounded than the usual comic book movie, It's still a movie about a man who dresses up like a bat to fight crime and will inevitably require "suspension of disbelief" in some areas. The nolanverse is nowhere near as restrictive as fans made it out to be.
Even if the body doesn't exactly look like Dr Pavel, The fact that it would most likely be burned beyond recognition means that an autopsy wouldn't really mean squat in identifying that it wasn't him, The stock market fraud would have been overturned eventually just not right away and they didn't send every cop into the sewers (as said by the priest who John Blake talks too).