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: Harvey Dent is on the telephone while smoking a cigar that is partly ash. Two camera angles later he is smoking a brand new cigar with no visible ash. (00:58:25)
Continuity mistake: At the beginning of the movie when the police are standing outside of Axis Chemicals, Eckhardt has very distinct facial hair. In the next shot when they are inside the plant he is clean shaven. (00:23:05 - 00:24:10)
Continuity mistake: At Axis Chemicals, Jack's face is cut by broken glass and has blood gushing out of it. But in the next shot, Jack (probably the stunt double) does not have any blood on him as he goes over the edge of the rail. (00:29:00)
Continuity mistake: In the alley, Bruce places two roses on a sidewalk and then walks away. But when Vicki gets to the roses, they have changed positions. (00:46:50)
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.
Continuity mistake: In the scene where Joker has broken in on the mayor's televised speech to the citizens of Gotham to challenge Batman to a "big duke-a-roo", Bruce freezes the live broadcast on a close-up of the Joker. He then flashes back to his parents murder. After the flashback, he looks again at the freeze frame picture of the Joker, but it is a different picture. When he freezes it, Joker's eyes are closed. When he comes back to the picture, his eyes are open.