Continuity mistake: In order to tiptoe across the tacks without being hurt, Tom puts a metal gauntlet on his feet. At this point, you can see the floor is completely covered in tacks, but when Jerry and Nibbles are at the same spot a little later on, the tacks have disappeared.
Continuity mistake: When Daffy is standing on the branch of the tree ready to jump off, he is holding on to a rope. When the camera angle changes to behind Daffy in the next shot, the rope is missing.
Audio problem: When Bugs says "I just hope I will be in one piece, so I can appreciate it", his mouth is not moving.
Continuity mistake: When Daffy rushes up to take his breakfast from Elmer, you can see the door behind them is closed, but when Elmer tells Daffy he's had enough, the door is now open.
Continuity mistake: When Bugs is climbing up the ladder, you can see that he has a toothbrush in his right hand, but when he enters the rocket ship, the toothbrush has disappeared.