Continuity mistake: When we first see Bugs' hole, you can see there are three carrot ends around it. After the dogs run over the hole, there are now only two carrot ends, and when the hunters pass over the hole, there are now three.
Continuity mistake: When the large hunting dog comes up to Bugs in his fox's costume, Bugs is holding a carrot in his left hand. But when he points his hand to tell the dog where the other hunting dogs went to, the carrot has gone.
Continuity mistake: When Bugs is eating his carrot and the large hunting dog starts sniffing on the ground, there is nothing in the background. But in a close-up of Bugs in the next shot, trees have appeared.