Continuity mistake: At Edward Nygma's party at the Ritz Gotham there is a fountain with a large version of his "box" on top. When Two-Face comes, he shoots the "box" and destroys it. There should be some parts left over but when Batman falls through the ceiling he lands on the fountain and there's no remains of the "box." (01:12:15 - 01:13:30)
Continuity mistake: When Chris O'Donnell does the laundry and is putting wet clothes on the string, he takes a clothing item and wraps it around his right leg then twists water out of it. When he does this his right foot goes in the air a few inches above the ground but in a closeup to his foot and water falling it is his right foot standing when it should be his left. (00:55:00)
Continuity mistake: In the scene at the circus when the ringmaster announces "The Flying Graysons", Robin's mom is standing on his left side. In the very next shot, she is on his right side. Also, when Robin is doing the "Death Drop", his mom is on his left and his brother is on his right side. After he completes the stunt and he swings back up with his dad, his mom and brother have switched places. (00:32:45)
Continuity mistake: In the scene in which Edward is first testing his "box", watch Ed's left shoulder. He goes to turn off the machine, then says his line "What a rush." The shot cuts to Ed's boss briefly. When the shot cuts back to Ed, his left shoulder strap, which was present in every other shot, is missing. He even reaches to take the strap off as he starts to say "A very surprising side effect." Apparently, he didn't even notice that it had fallen off.
Revealing mistake: When the Riddler projects the question mark above the bat signal, two beams can be seen producing the image, except they are slowly tracing the perimeter. If these beams are producing the image, it should only be visible where the beams are touching, and not everywhere else. In order to produce an image and not just two points, beams would need to travel extremely fast to trace the perimeter without leaving gaps. (much the same way images in a lasershow are produced). (01:33:10)Rosco
Continuity mistake: When Riddler and Two Face are stealing diamonds, the Riddler is holding a large diamond. Two Face comes over to him and produces an even bigger one. However, if you look closely at the shots, the diamond the Riddler holds gets smaller in one cut, and Two Face then pulls out the diamond Riddler was just holding...
Continuity mistake: When Bruce is reading the riddle about vowels, it starts out "We're five little items of an everyday sort." He pushes the button to read the second part of the riddle. Then when Bruce walks around, the first part of the riddle can be seen again. (01:33:25)
Continuity mistake: When Batman jumps up into the Riddler's lair, he's gone up the outside of the shaft - we see a shot from his point of view right up to the point of entry, and he's right at the edge. But when he jumps back into the shaft, despite not having moved, he's suddenly right in the middle of it.Jon Sandys
Continuity mistake: While retrieving the safe from the chopper, Batman tells the bank guard to "hang on." The guard holds on to the chain to which the safe is attached. But as the safe comes back into the vault, the bank guard is holding on to one of the tubular structures of the safe itself. (00:09:35)
Plot hole: In the scene at Wayne Manor where they show Harvey "Twoface" getting scarred with the acid on TV, you can see the acid cover almost his entire face before he puts the folder over to protect it. (00:24:15)