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.
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 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.
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.
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.