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: 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: 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 Bruce wakes up after getting shot in the head by Two-Face, there is a "BW" (Bruce Wayne) on his pillow next to his left ear. But after Alfred asks, "How are you, young man?", the "BW" is gone. (01:35:55)
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.
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.