When Robin pulls his face out of the pink goo, it actually pulls his mask down, away from his eyes. In the next shot, this mistake has been corrected and the mask is back in place.
After Joker sprays Batman on his insignia he signs it. It looks like 3 lines, but in the next scene there is a well-defined letter "J" on his bat insignia.
When Joker and his henchmen flee the art gallery, Robin asks Batman why he is letting them get away. Batman replies, "He has committed no crime." In fact, defacing paintings is an act of vandalism. Punishments range from community service to restitution to jail time.