Audio problem: In the early backstage scenes from the convention, the other actors are angry at Tim Allen's character. The actor who plays Laredo clearly says "You are so full of sh*t", but it is edited to "full of it." Those two word edits ('s' word and 'f' word) were done to keep the PG rating, but the editing is sloppy. [This theory could also be expanded to the drug reference mentioned above].
Audio problem: When the aliens are talking to Taggart at his house, in a shot from behind the aliens looking at Taggart in the doorway, the audio is out of sync with the alien leader's mouth. You can see this when he says the word "destruction."
Audio problem: When Brandon's parents are listening to the news reporter talk about the crew not showing up to the convention, his words don't match his mouth at the end of the shot.
Audio problem: When they are rolling the beryllium sphere into the ship, Laredo is heard yelling, but his mouth isn't moving.
Audio problem: Right after the Thermians become sad over the mention of Gilligan's Island, Alexander rolls his eyes and starts to turn away, while you can hear him saying "Oh brother." However his lips are not moving for this indicating the line was dubbed in.
Suggested correction: It's quite obviously Laredo/Tommy's voice saying "Oh, brother" off camera. Not Alan Rickman. Their voices don't sound anything alike. You can see for yourself at this clip at about 1:03: https://www.youtube.com/watch?v=26tWWopd_3g.
Suggested correction: It is not Alexander who says it, but most likely Guy.
No it's Alan Rickman's voice.
It's definitely not Alan Rickman's voice. It's Tommy/Laredo's voice off camera saying the line.
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)
Revealing mistake: When General Roth is threatening Jason with his claws wrapped around Jason's throat, the very moment he tilts his chin back, you can see the actor's open mouth and teeth visible inside, though he's supposed to be an alien enemy.
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)