Revealing 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)
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.
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.
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)
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.