Continuity mistake: When going to the Gotham City Bank, the clock tower bell will begin to ring. Alfred then contacts Batman and says that it's now 12:00 AM and wishes him a merry Christmas. If you look at the clock tower, however, the clock says that it's only 9 o'clock.
Other mistake: Even when you beat both Shiva and Deadshot they're shown on TV monitors at Joker's meeting in the penthouse suite of the Royal Hotel.
Continuity mistake: In the Batcave, when Alfred is telling Batman that he is a man, not an island at the end, Batman's cape is nowhere near him. In the next shot, it's on his back. The back of his mask also inexplicably appears as well.
Continuity mistake: Batman uses gadgets in Origins he doesn't get until Arkham City.
Answer: Maybe it's because he's a loose cannon who kills for money.
Rob245