Continuity mistake: When Daffy sends the Martian an ultimatum, the ultimatum goes back into a bullet and lands on the floor of the Martian's spaceship. But when Daffy sends him an ultimatum saying "Ouch!" there is no sign of the bullet.
Continuity mistake: When Duck Dodgers claims Planet X with his flag, you can see there is nothing next to him, but when Marvin the Martian comes along and makes his claim, an "X" tree has suddenly appeared.
Character mistake: On the sign outside Dr I.Q. Hi's headquarters, the word "Stratosphere" is spelled "Stratopere."