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...
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 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 Edward Nygma meets Bruce Wayne his hair is messed up around his forehead. A shot later it's nicely combed.
Continuity mistake: When Bruce asks the doorman where Dr. Meridian is a man walks down the steps and leaves. Shot changes and he is walking down the steps again.
Continuity mistake: In the fight scene outside the elevator at the beginning of the movie, there are at least two shots where you see Batman's back without his cape in the way. There are no items whatsoever attached to the back of his belt. Subsequently he manages to pull the stun device and the grappling gun with grappling hook from behind his costume. A previous corrector proposed that the devices could not be seen because they are concealed in "pouches" on Batman's belt. Close inspection of the scene shows that there are no pouches of any kind on his back or concealed in his cape.
Continuity mistake: Two-Face and the Riddler are in Two-Face's lair; the Riddler has just said, "Then I taught my doggie a new trick; how to map the human mind." In the establishing shot, the tube is in left hand; after the cut, it's in his right hand.
Continuity mistake: When Dick Grayson is showing off his fancy laundry skills, he splashes water onto the washing machine and dryer. In the last shot when he mops up the mess, the water is gone from one side of the machines.
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: In the beginning Batman suits up with a heavy leather-like cape. When he swings to the street his cape flaps and ruffles in the wind like thin silk; very obviously a completely different material.
Continuity mistake: When Bruce has just gotten shot by Two - Face and Riddler has just put the vowel riddle down, the riddle has a short stick with Bruce's head on the top to be a tennis ball. When they're taking Dr. Chase away, the bird's eye shot of Bruce laying shows no stick.
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.
Continuity mistake: When the holographic floor disappears in Nygmatech, Batman is standing on a U-shaped "plank" extending out over the open pit. Cut camera angle to a shot looking up at him and he's jumping from a flat ledge; the U-shaped plank has disappeared.
Continuity mistake: When the Riddler has Chase prisoner on his sofa, the chains on her feet have padlocks at the beginning of the scene; then the padlocks disappear when he says, "Like the jacket," and appear again when Chase says Batman will come for her.
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.
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.