Deliberate mistake: When the CA. trooper is at the front of her car, the Arizona license plate is shown. In 1989, Arizona began issuing a single license plate and that plate is always on the back of the vehicle. This is deliberate, as the remake follows the original movie shot by shot, and there the trooper checks the front license plate.
Deliberate mistake: The car that Marion buys has a current California license plate with the number NFB 418, which matches the number from the original movie - but at the time, California plates would have had another digit before the letters; probably a 3, i.e. 3NFB418.