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.
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.
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: 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.
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.
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."
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.
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.