In one shot, as the Joker drops through the trap door to escape the museum of modern art, his hair is brown, not green.
When Batman is christening the boat, he mentions that the champagne is from 1949, but when he's telling Joker how he found out about his plan, he says it was from 1849.
Chief O'Hara remarks that he never thought he'd see the day when the Joker was content to play baseball instead of plotting a prison break, however, the prisoners are playing softball, not baseball.