Continuity mistake: When Sam confronts Bugs by the Powder Room, Bugs takes out a match, lights it and throws it into the Powder Room. You can see that the packet of matches is now one short. When Sam tells Bugs that "If you does that once more, I ain't a-goin' after it!" we cut to Bugs and when he takes out the packet, it is now full with matches again.
Continuity mistake: When Sam is squashed by the mast, his axe lands on the deck. When we see a squashed Sam in the next shot, the axe is nowhere to be seen.
Continuity mistake: When we see Sam wandering on to Bugs' ship he has nothing in his hand, but when he comes to the mast he is now holding a sword.
Continuity mistake: When Sam swings into Bugs' cannon, he is holding a sword in his right hand. When he tries to retreat, the sword is missing, and after he is blasted by the cannon, the sword is back in his hand again.
Continuity mistake: When Bugs climbs out of the crate full of carrots, he has a carrot in his right hand. When he goes to ask Sam "What's up, Doc?" the carrot has gone.