Other mistake: The shot showing the vault swinging back to his location is the same that the one where the vault is swinging out, but going backwards.
Other mistake: When Batman puts the lit torch to the cable and the cable breaks; the vault goes back into exactly the same place where the helicopter lifted it out from; connected via a grapple that Batman put through the wall. Ignoring the logistics of how this would be possible, it tightens the grapple, which surely, with the weight of the vault, would have ripped itself away from the wall.
Other mistake: The headline of the newspaper says about Two Face robbing Nygma's party and Batman saving the guests, but the body of the text is about Thomas Wayne's death.
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.