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.
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.
Continuity mistake: When the girl climbs out of the prison her head gear is not joined under her chin. In the next shot when she covers her head, the bottom is now joined together.
Plot hole: During the chase after the stock exchange attack, Batman ends up flying the batwing out from an alleyway after being chased there by police. But it can't fly itself (part of the plot) and the attack took place during the day, meaning that even if Batman somehow planned for this, he must have just stuck the batwing in an alley for a fairly long period of time and somehow no-one stumbled across it, despite being in a busy part of the city.
Revealing mistake: When Bane first breaks into the stock exchange, he forces one of the guards into shooting his gun. Two mistakes: there is no flash or muzzle flare, and the gun has an insane amount of recoil. It's not a cannon, it's a 9mm. It's also not the guard being startled by Bane: Bane is the one holding his arm.