Revealing mistake: When Jack is hanging out of the truck you can see him standing on the hood of the car which Lydia is driving. At some points we get camera view from the back seat of the car. In some angles the mirror inside the car disappear. This is to prevent us from seeing the camera.
Continuity mistake: When Jack is having a seizure at his job he stuff some aspirin in his mouth. When the manager says "He is spaced out." it cuts to the girl saying "I'll handle this.". At that point Jack has got two aspirin hanging out of his mouth. It cuts and the aspirins are gone.
Continuity mistake: Just after the scene where Jack Putter gets tazed by Lydia Maxwell in the restaurant, Mr. Igoe initially hauls the unconscious Putter over his left shoulder. In the following shot you'll notice that when he exits through the back door, he's carrying Putter over the right shoulder. This mistake was pointed out by the director (Joe Dante) himself on the commentary track of the DVD version.
Continuity mistake: When Pete and Dr. Niles are in the car discussing the project, the background keeps changing depending on the camera angle. They're suppose to be stuck in traffic, driving near a giant hillside. But in some angles there's no cars next to them and it's wide open space with no sign of the hill. And the cars around them change.
Revealing mistake: In the scene where Jack and Lydia are driving and the miniaturized Drs. Scrimshaw and Margaret are fighting them in the front seat, the washer fluid is spraying on the windshield, but it's not being blown around by the wind at all (indicating the car is stationary in front of a blue/green screen). A few seconds later, the scene cuts to Lydia and back to Jack and the washer fluid is off and the windshield is dry.