Continuity mistake: When Bruce plays the clip of the Joker appearing at the rooftop party, the audio clip that plays with it is not the same as when the Joker actually said it during the attack. The clip seems a bit more subdued than the actual voice track.
Continuity mistake: During Barbara Gordon's flashback to when Robin went missing, when Batman and Batgirl enter Arkham Asylum, Harley Quinn alerts the Joker that they have company. The Joker is seen with a pipe in his mouth. He takes the pipe into his right hand as he starts to come down the stairs. In the very next shot, the pipe is missing. (00:37:20)