Other mistake: When you play the DLC side mission "Wonderland," notice all three missing cop cars have the same license tag.
Plot hole: In the DLC side mission In From The Cold there's emphasis put on Mr Freeze detonating the cryogenics generator he's been using in his research to take out militia tanks. Given they and almost all the icebergs explode it's amazing the Batmobile avoids instantly sinking into Gotham's waters.
Batman: I am vengeance. I am the night. I am Batman.
Trivia: When Batman enters the clock tower, there's a flashback scene of Barbara being shot by the Joker. Before this occurs, go to the back wall and zoom in on the movie poster, "Dark Interlude." One of the names on the poster is Matthew Hagen. In "Batman: The Animated Series", Matthew Hagen was an actor who was transformed into the shape shifting villain Clayface.
Answer: As a child, Jervis Tetch never had any friends. Even in his adult years, he was all alone. When Jervis asked Batman to be his Alice, he was essentially asking Batman to be his friend.