Continuity mistake: When Steve Brody comes and sees the Swami after being thrown out of the gambling establishment, he has a plaster on his face. But when the Swami says "There's the answer" the plaster has gone, and in the next shot it is back on Steve's face again.
Continuity mistake: When Bugs rolls the dice during the gambling scene, the dice land on the table and the other gamblers take their money away. But when we see Steve and Bugs in the next shot, the dice are no longer on the table.
Continuity mistake: Bugs dresses up as a man with a carnation and you can see he has a pink carnation on him when he meets Steve Brody for the first time. But when Bugs says "What's up, doc!" to Steve later on, he has no carnation.