Continuity mistake: When Gazoo crash-lands his flying saucer, the top portion of his helmet and his antenna are shown to serve as the roof of the spacecraft. This is what Fred grips to try and open the saucer. While attached to the saucer, the top of the helmet is completely smooth except for the antenna sticking up. However, once Fred has loosed Gazoo from the ship, Gazoo's helmet now has a prominent ridge running the entire length of the helmet from front to back. This ridge should have been, but wasn't visible while Gazoo was still in the ship.
Continuity mistake: In the first movie Wilma rips off her pearl necklace after a fight with Fred, saying that she doesn't need it, as it was a present from Fred. However in this movie it is shown that the necklace was given to Wilma by her father.