Other mistake: When Two-Face flips his coin in the air to decide whether or not to kill Rupert Thorne, Batman is surveying his surroundings, finding a box full of silver dollars and laboriously tossing the box into the air in order to make Two-Face lose sight of his coin. In the time it took Batman to do that, Two-Face's coin would have already landed back in his hand.
Other mistake: When Two-Face is looking at the picture of Grace in his wallet, you can see he has a credit card that says Two Fa[ce]" on it. A bank wouldn't issue a credit card to someone under that kind of pseudonym, and it would be very foolish for a known criminal to use a credit card since any purchases can be tracked. Even if it was a company credit card for a dummy corporation, it would be equally foolish for Two-Face to have a dummy corporation named after himself.