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 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.
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.
Continuity mistake: Sarris' lieutenant Lathe is in two places at once during the siege of the Protector. He is seen in the atmosphere control room when the rock monster is beamed in and presumably dies later. A few moments later, he is on board Sarris' ship informing him that the crew has escaped custody.