Continuity mistake: At the beginning, Buckaroo tests his oscillation overthruster. Sitting in his test vehicle he's wearing a wrap-around mirrored visor that reflects a full panorama of the desert area in front of him. There is a thick black divider running down the center of the windshield that is missing from the reflection. Also, since it is a panorama seen on the visor, the edges of the front windshield should be reflected on the sides.
Continuity mistake: The social worker takes "the brother" to stay for a while at a female friend's place. Her son, "little Earl" has a bandage on his left knee. He peels the bandage off and sets it on the floor to show "the brother alien" his injury. A medium shot shows there is no bandage on the floor. The "alien" puts his hand on the boy's knee, and heals it. The very next shot the bandage is back on the boy's knee and the scene continues.
Other mistake: When they're walking on the Tri System, you can see the wrinkles in the fabric used to create the foggy background.
Continuity mistake: Towards the end of the movie, when Josh and Holly are trying to escape in the car, a mutant is on the roof and starts melting its hand through the windshield to get at Josh. The mutant is leaning over the windshield with its hand sticking through a hole it melted in the glass. In the next shot as they round a corner, the mutant is suddenly towards the back of the roof of the car, just holding on without attacking the windshield. In the next shot, the hole is gone also from the glass. (01:25:45)