Revealing mistake: In one scene, the Penguin is making a "bat" shadow puppet on the ceiling. But there's no light behind his hands. If there's no light, there's no shadow.
Continuity mistake: When Selina returns home from work she takes milk out of the fridge and pours her cat some, leaving the carton on the worktop. She then runs to work, and when she returns after being changed to 'catwoman', the milk has vanished from the worktop. The dishes also move and plant pots appear on the window sill.
Revealing mistake: When the Penguin drives the Batmobile remotely, the cars it smashes are damaged just before it hits them.