Continuity mistake: When the Riddler blows up the Batmobile, if you look closely, you'll see its rear left wheel cap fell off at different angles.
Revealing mistake: When Two Face and Riddler enter Wayne Manor, and knock Alfred down. Alfred, unconscious, pushes the dinner tray aside, so the thugs can carry him into the closet. (01:27:55)
Continuity mistake: In the scene where Robin steals the Batmobile, the first shot of his joy-ride shows twin fins on the rear of the batmobile on 45 degree angles, in the following shots they are all standing directly vertical. (01:02:40)
Character mistake: When Bruce is looking at Chase's various clippings of Batman on her desk while she's tending to the tea kettle, there is a paper that says "Diagnosis Form #39," and just above it, the word "schizophrenic" is incorrectly spelled as either "schizofrenic" or "schizoprenic" (a metal clip is partially covering the last six letters of the word, so it's hard to determine whether it's an "f" or a lone "p" where the "ph" should be). (01:03:11 - 01:03:32)
Continuity mistake: At the end of the film right after Batman has saved Chase and Robin from falling and Two-Face appears on the ledge, you can see that in one shot Chase has lost her shoes and in the next shot she's wearing black sneakers. (01:48:00)
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: 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: Right before The Riddler is about to kill Robin and Dr. Chase, his finger changes position on the button on his cane between shots. In one shot it is next to the button but in the other it is suddenly completely covering the button. (01:57:15)
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: When checking a tape that shows the (fake) suicide of Stickley, Bruce is handed the suicide letter, which was folded in three parts. The next shot shows a clean sheet of paper, with no wrinkles or folds. (00:26:20)
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.
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...
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)
Continuity mistake: When Two-Face and his goons are fleeing Nygmatech after their break-in, as they're running down the stairs there are 3 men in identical blue suits running just ahead of Two-Face. In the next shot they're nowhere to be found.
Continuity mistake: When the Riddler and Two-Face are in their getaway van after robbing the jewelery store, the Riddler has his green hat on, but in the next shot, it has switched to a tiara. (00:55:40)
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)
Audio problem: When boiling acid starts spraying inside of the bank vault that Batman and a security guard are in, the security guard shouts "It's boiling acid." But his lips does not match with what he is saying. It happens again when the guard yells to Batman, "Don't let go." (00:08:15)
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.
Continuity mistake: When Nygma is reading his boss' mind he pulls the lever to add more power. The way he holds it differs between shots. (00:20:22)
Continuity mistake: When Edward Nygma meets Bruce Wayne his hair is messed up around his forehead. A shot later it's nicely combed.
Chosen answer: Batman talks like that because if he talks like Bruce Wayne (Val Kilmer's voice) his voice might be recognized, leading to Batman's identity being revealed.