Continuity mistake: When Guy is introducing the actors at the start of the movie, while he is saying Jason's name, to the right of the screen you can see that Guy is holding a glass of water with lemon. The camera then cuts to an overhead shot of the whole crowd and Guy can be seen clapping with nothing in his hands.
Continuity mistake: When they are rolling the beryllium sphere back to the ship, Fred has his paper bag in his mouth in some shots and it disappears completely in others.
Continuity mistake: When Jason gets in the limo with the Thermians, the limo starts off having no license plate and changes to a California plate between shots.
Continuity mistake: At the end, when the crew is bowing to the fans, Sigourney is shown moving her right leg back a small bit. However, when they show them standing up from the bow, her right leg is fully crossed behind her.
Continuity mistake: When Fred is giving Guy the "comic relief" pep talk, his left hand is on the left side of Guy's chest, but then the view changes to Guy's right side and Fred's left hand is now on the right side of Guy's chest, where it remains until Fred turns Guy and they walk out of the scene.
Continuity mistake: When the 4 "nerds" first approach the captain to talk about their supposed problem the girl is standing in a different place than when they cut back. In a later scene the girl is in this position and I believe they reshot the earlier scene while they were doing the later scene. (00:07:30)
Continuity mistake: During the opening sequence of Alexander storming out of the back rooms, you can see Tommy help keep him there. However within the next shot as they Call Gwen to the stage, you can see Tommy and the whole crew out on stage but Alexander and the Commander are still having the same dialogue. (00:04:10 - 00:05:00)
Continuity mistake: When they're flying down to the planet, Guy is upset because he doesn't have a last name. He asks Jason, "What's my last name?" and Jason doesn't know. In the very next scene, Jason addresses Guy by his last name, Fleegman. (00:55:00)