Continuity mistake: After Batman rescues Vicky he has a voice remote for the Batmobile. As the car approaches he orders the car to stop by speaking into the remote and then lowers it to his side. When the camera shot changes showing the car stopping right in front of him, he is still holding the remote to his mouth. (01:09:20)
Continuity mistake: When Joker is at the top of the building and taunting them, his chin is red (presumably from his blood when Batman socked him in the jaw.) After he falls off the building, and we see him lying on the ground, his chin is not covered in blood like it was before. (01:50:45 - 01:54:35)
Continuity mistake: When the "automated" Batmobile is sent into Axis Chemicals to blow it up, six of the Joker's men are shooting at it before it explodes, killing or seriously injuring everyone. Three of these same henchmen are also on the Joker's parade float at the very same time or very shortly afterwards in Gotham Plaza and one of them flies the Joker's escape copter at the end of the movie.
Continuity mistake: When Batman jumps off of the remaining bell at the top of the cathedral, the goon uses Batman's momentum to throw him into a set of stairs, his trajectory parallel with the near wall. Since the goon wasn't standing near the wall when he threw Batman, this angle would not be possible to achieve.