Continuity mistake: When Bugs takes out the bubble gum, you can see he is holding the gum between two fingers and a thumb. But in a close-up, he is holding the gum at the bottom of the wrapper.
Continuity mistake: After Sam is hit in the face by the rock, the rock lands by Bugs' hole. When Sam returns with a spade and starts digging, the rock has gone.
Continuity mistake: When Sam is putting wood in the oven, Bugs tells him to put a log in because he "loves the smell of old hickory." At this point, you can see there are some logs under Bugs, but in the next shot they have disappeared.