Continuity mistake: When going to the Gotham City Bank, the clock tower bell will begin to ring. Alfred then contacts Batman and says that it's now 12:00 AM and wishes him a merry Christmas. If you look at the clock tower, however, the clock says that it's only 9 o'clock.
Continuity mistake: In the Batcave, when Alfred is telling Batman that he is a man, not an island at the end, Batman's cape is nowhere near him. In the next shot, it's on his back. The back of his mask also inexplicably appears as well.