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.
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: 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.
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 henchmen 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.
Continuity mistake: As Batman begins to approach Bane during the final battle, be on the look out for a certain extra (a middle-aged man with a grey beard and brown vest). You'll see him fighting behind Batman...only to be seen fighting behind Bane in the very next shot.
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.
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."
Continuity mistake: During Bane and Batman's first battle Selina is behind Batman when the fight starts, then Bane's back is to her later, but Bane and Batman don't switch positions on the catwalk.
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.