When Bruce Wayne picks up Selina Kyle for their date, she is wearing a strapless periwinkle blue dress. When they get back into the car after meeting with Stern, she is wearing a purple dress with a collar under her grey jacket.
When Catwoman throws Batman off the roof and he saves himself by grabbing a ledge, the Bat-insignia on his chest is missing.
A white dot can be seen on Batman's upper lip in the opening sequence on the close up of Batman's face. It was admitted during a commentary that it was discovered too late and could not be fixed. This is in all opening sequences.
The notes you see played on a keyboard don't match the notes heard.