Continuity mistake: In the vault, just before Batman enters, we get a nice shot of the bank guard. He appears to be lying length-wise in the vault, his body flat and straight, and his head laying on the "step" toward the left side of the screen. When the scene cuts to Batman entering the vault, the guard is positioned differently, at much more of an angle, and his head is higher, closer to the second row of boxes from the bottom of the vault. (00:07:25)
Continuity mistake: In the part after The Riddler shows Two-Face the newspaper with the headline "Batman Survives Subway Sabotage," The Riddler pushes a glowing green cylinder into the monkey's mouth and the camera cuts to the screen so they can see Bruce Wayne's brain. When it cuts back to Two-Face and The Riddler, the cylinder isn't there. (01:25:54)
Continuity mistake: After the Bat-Boat is destroyed, it changes to a normal wooden boat. (01:41:50)
Continuity mistake: In the dream/memory where young Bruce is falling into the cave, the red book is in his right hand as he starts to fall. It is dark and raining. The next shot shows him at the top of the hole falling and he has dropped the red book. It is also bright outside with no signs of rain. The next shot shows him with the red book in his left hand. When he stands the book is in front of him, too far away if he held it. (01:30:00)
Continuity mistake: When Bruce slides across the table, both pumpkins go the right near Dr. Chase. In the next shot, they are on each side of the table. (01:32:55)
Continuity mistake: When Edward Nygma is in his apartment after killing Stickley, we see him pasting letters for the next riddle involving the match head. However, when Bruce and Chase are in her office looking at the riddle after it was delivered, you can see the letters are in different positions than the earlier shot.
Continuity mistake: Bruce's hair is much flatter and messier in the garage than in the previous scene outside when Dick is leaving, even though the garage scene happens directly after.
Continuity mistake: As the giant safe is being pulled out of the building, a large section of the wall above the hole breaks and starts falling outside the building. The shot cuts to outside and the hole is now back to the same size as before and no chunks of wall are falling. There aren't even any cracks where a piece might break off.