Continuity mistake: When Bugs is hopping around, Elmer does not have anything in his left hand. In the next shot, he is holding his gun, and in the shot after that, the gun has gone again.
Continuity mistake: Elmer is standing by a hole when Bugs is hopping around, but when he tells the audience that this fellow is a "RABBIT", we cut back to Elmer and the hole has gone.
Continuity mistake: When Elmer chases Bugs, Bugs runs into his hole and Elmer drops his gun by the hole. But when Bugs kisses Elmer, we cut back to him and the gun has disappeared.