The station wagon Butch steals is a either an Oldsmobile Vista Cruiser or its twin the Buick Skylark Sports Wagon, easily identified by the glass "skylights" around the edge of the roof. However these cars were not introduced until February of 1964. Earlier in the movie a reference is made to an upcoming visit to Dallas by President Kennedy, so the car could not exist during the time frame of the movie.
Based on the references to President John F. Kennedy and the Texas governor's re-election campaign, the events in this movie take place in 1962. The US paper money shown at the end of the movie and in the opening are modern post-1964 Federal Reserve Notes instead of Silver Certificates which were the only currency in circulation in 1962.
When Butch is blocked by the police car in the alley he puts the car in reverse and rams the squad car without any damage to his own. In fact, throughout the whole ordeal with the two squad cars he manages to keep the car from being damaged at all.
When Butch is fleeing the police after leaving the store and smashing the police cars, they chase his car into an alley behind some buildings. He cuts the wheel left and gets into a wild skid and you see the hubcap come flying off the passenger side front wheel and roll away. But in the next scene, and the whole rest of the movie, the hubcap is back on the wheel.
In the standoff scene Laura Dern is shown from the front looking through binoculars. An instant later she is shown from behind and she has her arms at her sides and is not holding any binoculars. Another instant later she is again shown from the front and is once again holding binoculars.
in the scene where Red "requisitions" the governor's trailer to use on his manhunt, the first thing he does is tear off the red white and blue bunting from the side of the trailer. The bunting on the rear of the trailer was left in place as you can see when they drive away. In a subsequent scene where the profiler is speaking privately with Red inside the trailer, you can see the bunting outside the window that Red had previously removed.
Terry Pugh fires his revolver two times at the kidnap site, two times at the water tank and shoots two bullets through the car roof. So the revolver is empty when Phillip has to aim it at Pugh. When Pugh recovers the revolver he checks to see whether it is really empty. It is, but not only the bullets but also the empty shells are gone.
The goof item below may give away important plot points.
The wad of money Butch tucks into Phillip's Casper costume changes position several times between shots. Also, after Butch is shot and killed and Phillip is led away across the meadow, the money is shown falling out of his costume and being scattered by the breeze. However, when Butch is shown dying in the prelude and in the final scenes, many of the bills have mysteriously returned to the grass around his body.