Other mistake: When Chris is sleeping in his yellow car during the thunderstorm, he gets hit by a flash flood. Afterwards he abandons his car and removes his licence plates. His plates are: UW4-924. A few minutes later his parents decide to visit Chris in Atlanta. We then see a shot of a white car on the freeway, which has the exact same licence plate (UW4-924).
Factual error: There is a shot in which Christopher/Alexander Supertramp looks up towards a railroad trestle. You see four Burlington Northern Santa Fe locomotives. The story takes place in the early 1990's, and the Burlington Northern and Santa Fe railroad companies had not merged yet. They merged in 1995. They have gone through a couple different locomotive paint schemes since then and the one shown in the shot is a modern day one.
Continuity mistake: When Chris is in the trailer with Tracy, he walks inside with his towel around the back of his neck. During the scene he takes the towel off, then when we see a shot from behind him later, the towel is still there.