Continuity mistake: When they are all in the trailer chasing Butch's car, the trailer shakes and smashes about, but when you see the view inside the trailer the passengers are not even moving or anything in the trailer moves.
Continuity mistake: When Butch and Phillip reach the end of the tarred road they stop directly in front of a signpost. Towards the end of the scene there are some shots where the distance to the post is at least five meters, and also from the position of the steering wheel one can tell that the car has been moved in between. (01:01:50)
Factual error: One character refers to the mobile command post in the Airstream trailer as "high-tech", a phrase that wasn't around in 1963; "space-age" would have been more correct for the period.