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.
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.
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: When Selina has Daggett pressed up against a wall and we've seen her heels, Stryver points a gun at her and he says "Nice outfit, those heels make it tough to walk?" Shortly afterwards she and Bruce fighting Bane's goons on the roof, and she is now wearing flats.
Audio problem: Inside the well, when Bruce is about to take the final leap, the inmates are heard shouting "Rise!" in one single perfect cry, yet when the angle focuses on them no-one's mouth is in sync with the sound. Furthermore, no one's mouth is in sync with the inmate next to him.