Continuity mistake: When Bugs is putting wood into the oven, the left hand door is open. When he says "I couldn't do that to the little nimrod", we return to the oven and the left hand door is now closed.
Continuity mistake: When Sam takes out a burning log from the oven, you can see the right hand door is closed. When Sam tells Bugs to go into the oven, the door is now open.
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.
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 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.