Other mistake: In the scene at the beginning, when the robbers take Harold's wallet, the robber who had the gun says "American express card" but, when he says "don't leave home without it" the subtitles say the goon on the left says it, even though you can see the goon on the right move his mouth. (01:04:30)
Continuity mistake: While Bruce is talking with Vicky at the Batcave he is clean shaven, but after he attacks Axis chemicals he has some stubble on his face.
Continuity mistake: During the Batmobile car chase scene, Batman bangs a left from the side street near Monarch Theatre, leading Joker's henchmen and several patrol cars on a straight path for a few seconds. But right before the car pileup in front of Monarch Theatre, Batman is seen turning left onto the very same side street he came from to begin with. (01:08:00)