Character mistake: As Bruce Wayne is researching the jewel thief, the word "Heist" is spelled "Hiest" in a newspaper headline. (00:15:45)
Factual error: When the bridges are blown up, some of the bridges are suspension bridges, but the bridge only fails at the point of the explosion. The main horizontal supports are severed, but large portions of the bridge remain magically aloft. The nature of suspension bridges means the remaining vertical cables and road deck would fail as well, resulting in the loss of the bridge between the two main pillar supports.
Continuity mistake: When Bruce is meeting with Lucius in the office at Wayne Tower, the book on the seat next to Bruce changes positions during their conversation. (00:37:15)
Continuity mistake: During the stock exchange scene, after Bane says "Time to go mobile", the man with the laptop closes the laptop in the background and then does it again in closeup.
Continuity mistake: Catwoman puts her goggles on, shoots the batpod cannons at the car barricade, and in the immediate next shot they are back on the top of her head without her putting them there.
Continuity mistake: The fuselage of the plane is hanging straight down when Bane exits with the doctor, but it should be at an angle to the left, as we see when they are dragged behind the bigger plane.
Other mistake: When Catwoman and Batman are fighting Bane's henchmen on the rooftop, pay close attention to the guys in the background right before Batman knocks Catwoman's gun away: you can see that the henchman well out of Batman's reach on the far left falls over like he's been hit by a punch, but he couldn't be. Also, no gunshots are heard at that point, so he couldn't have been shot either. (00:53:30)
Character mistake: When Bruce is looking up information on Selina Kyle on his computer in the Batcave, at one point, "Kyle" is misspelled as "Klye."
Other mistake: During the fight later in the movie, when Batman stops Bane's henchmen from executing Blake, during a shot of Catwoman crouching, one of the henchmen behind her on the left of the screen just falls backwards, seemingly without being harmed in any way. If you look at the fight closely, it seems that it could have been intended for him to be the victim of an accidental gunshot to the leg that ended up not being followed through in post production.
Continuity mistake: It's a bright sunny day when Bane enters the stock exchange. When the police turn up moments later it's raining, with a wet road and puddles. When Bane exits on the motorbike, the roads are bone dry.
Revealing mistake: When Blake and Gordon watch Bane on TV during Gotham's siege, a grey (sometimes white) square is reflected on Gordon's glasses. It's either a lighting screen or the proof that the TV is turned off and the image on it is added on post-production.
Factual error: In the scene at the airport just before Selina Kyle is arrested, an Easyjet plane can be seen outside parked on the apron. Easyjet do not fly to the USA. The scene was filmed at Stansted Airport in Essex, from where Easyjet fly most of their European routes.
Audio problem: When Batman and Bane are fighting on the bridge, 3 punches before Batman falls over the bridge, he swings a punch at Bane where he misses by far, yet the sound is heard and Bane reacts to it.
Visible crew/equipment: Whilst the police are shown standing on the street, ready to fight Bane's mercenaries, just after Foley walks to the front of the crowd, it cuts to a shot of the mercenaries arriving on the street. In this shot, towards the left of frame, a man can be seen walking up a flight of stairs, carrying a radio. This man is not part of Bane's army and has no other reason to be present in the scene, so he is most likely a crew member that unintentionally walked into the shot. (02:11:00)
Audio problem: When the first stock broker is shot, the time between the shot and the recoil is far too long; over half a second, when it should have been instantaneous.
Continuity mistake: When Bruce meets with Lucius in his office his hands change from being on top of his cane in one shot to being just below it in the next.
Continuity mistake: When Selina has Daggett pressed up against a wall, she is shown wearing heels, but later on in the same scene, whilst she and Bruce fighting Bane's mercenaries on the roof, she is wearing flats. (00:52:00 - 00:53:25)
Visible crew/equipment: When the sewer explodes and the explosion comes up through the manhole surrounded by police officers, the cop nearest to the explosion can be seen wearing some sort of jelly to protect himself from the explosion. (00:23:30)
Continuity mistake: The bleachers in the stadium are semi-empty in the aerial angles, but packed with people in the close-ups.
Revealing mistake: During the party, the second time Gordon gives a speech praising Dent, a lighting screen is reflected on his glasses, which disappears in opposite shots.
Chosen answer: Given that no accurate records would have been kept of what occurred in Gotham during Bane's occupation, it would be very easy to claim that Bruce had been in the city when the bridges fell, been captured and subsequently executed by forcing him out on the ice, as had happened with many other socialites. Plenty of people died during Bane's takeover of the city, particularly in the final hours. There's no reason why Bruce would stand out among them as a candidate, and even if anybody did harbour some suspicion, it could hardly be proven.