Factual error: The bat signal at the end of the film defies physics. The spotlight is a few feet across and is projecting the signal onto clouds far above. To do this, the light beam should get wider as it climbs up (like a flashlight's beam aimed at the ceiling). Yet the shot of the clouds shows rays of light getting wider as they go downward, like sun rays through the clouds. For this to exist, there's either a bat signal floating far above and through the clouds, or the one on the roof needs to be several miles wide, focusing a beam that narrows as it climbs.
Continuity mistake: When the Tumbler leaps toward the steeply-angled rooftop (the shingled roof with dormers), beyond it is a tall office building on the opposite side of a highway that is running perpendicular to the Tumbler's direction of travel (and parallel to the face of the office building). In order to leap onto this highway, the Tumbler will need to make a hard left or right turn, as going straight will take it across the highway into the face of the office building. But as the Tumbler reaches the end of the angled roof, suddenly the office building has moved far to the left, and the highway is now nearly in line with the Tumbler's direction, running into the distance next to the office building, and passes along the left side of the shingled roof, making it easy for the Tumbler to leap easily onto the roadway.
Continuity mistake: When Batman is chased by the cops while he is trying to save Rachel, he reaches the roof of a parking lot and stops. A cop orders him to switch off the engine of his vehicle and get out. Later when Batman is chased inside a tunnel, we see a cop asking on his radio what the Batmobile looks like. The Batmobile then zooms past him and he says "never mind". The only problem is that it's the same cop both times, so he knew full well what the Batmobile looks like when it stopped in front of him initially. Probably caused by the order of those sequences being switched in editing, but still a mistake.
Continuity mistake: During the training exercise on the ice, just after Ducard says that the parents' deaths were Dr. Wayne's fault, Bruce gets up and launches after Ducard in anger. In the shot from the front, he doesn't wear any scarf. The next shot from his back reveals that he is wearing a red/gray scarf over his jacket.
Continuity mistake: When the thug attacks Bruce in the beginning of the movie, the man grabs his hair, yanking it straight up. In the next shot, he's suddenly yanking it sideways. His action is shown in real time, visible on screen at all times, and therefore can't be corrected by saying it only takes a fraction of a second to move his hand.
Revealing mistake: When Batman flees from Gordon after their first meeting, he leaps across an alley and catches himself on the railing on a fire escape. This fire escape fails, dropping him (as well as the clothing left to dry on the railing). Batman grabs the next railing and again, this second fire escape collapses. Exactly the same as the first, with the same clothing falling off. When he climbs onto the 'third' fire escape, we see he's only come down one level, not two. The scene was artificially lengthened by using two perspectives of the same stunt. This isn't the same as showing one explosion from multiple angles because it is timed/edited precisely to appear as a longer fall in continuous time, not as repetition of the same moment.
Continuity mistake: Before Alfred knocks down the man outside the burning mansion, there are several shots from the inside of the building. In one of them, there's a burning table with a globe on. When Alfred and Bruce escape, they enter the room with the piano, and the same table is seen again. There are lots of flames around the table, but the table itself is no longer on fire.
Continuity mistake: When Sergeant Gordon puts the jacket around a young Bruce, the jacket is lying smooth around Bruce in the first shots. In the consecutive shot where Gordon says, "It's okay" for the second time, there's suddenly a huge bulge in the jacket on Bruce's left shoulder, but in the next shot, the jacket is smooth again.
Continuity mistake: When the young Bruce is trapped at the bottom of the well, there are several shots looking up from the bottom. In the first shot, branches are seen over the well. When the bats fly out of the well, there are different branches, and when Thomas Wayne lowers himself down to rescue his son, yet another set of branches is seen.