Continuity mistake: When the man from the draft board says "Well now, I wouldn't say that!" to Daffy in the closet, Daffy has one hand on the handle. In the next shot, he can be seen holding the handle with both hands, and in the shot after that, he is holding it with one hand again.
Continuity mistake: When Daffy takes off on his rocket, you can see the rocket has two red rings around them. But when we see Daffy plunging back to Earth, the red rings have gone.
Continuity mistake: When Daffy packs his cases to escape the little man from the draft board, he packs two cases. But when he opens the door and sees the man, he is holding only one case.
Daffy Duck: I guess he's gone now.
The Little Man from the Draft Board: Well, now, I wouldn't say that.
The Little Man from the Draft Board: Good heavens. That was quite an explosion. Are you hurt, son?
Daffy Duck: Oh, I'm a little shaken up, but you should've seen what happened to that dope from the draft board. He was blown to smithereens, see? Smithereens.
The Little Man from the Draft Board: Well, now, I.
Daffy Duck: No! No! You wouldn't say that! It's you! It's you.