Continuity mistake: At the Gator Motel, after Cledus and Bandit get part of the money, when Bandit starts crying about Frog and blows his nose into the money, there is a side shot showing a wad of bills in Bandit's shirt pocket before he actually puts the bills into his pocket in a following shot. (00:12:45)
Continuity mistake: When Sheriff Justice has caused the roller coaster frame to collapse his car's left front hubcap is gone, but soon reappears. Then during the "game of chicken" between the semi-trailers and police cars, his car's left back hubcap is gone, but reappears just before Justice thinks about retiring.
Revealing mistake: When the sheriff's car is flipped upside down, the sign behind the car is upside down too, so you can tell the car isn't really upside down.
Continuity mistake: When Buford T. Justice's car goes off the drawbridge, it is a different older body style car than what he was driving originally.
Revealing mistake: When Sheriff Justice's car falls off of the drawbridge, there are ropes visible on the sides.
Revealing mistake: Right after one of the Mountie's cars is split in half by the snowplow, you can see the mini-wheel used to keep the half-car propped up.
Revealing mistake: When in the desert crash scenes, there is a side on view of a garbage truck lifting up a Police car and dropping it into its bin on the back. In the foreground is an upturned Police car that another car vaults over and crashes. You can see the ramp in front of the upturned car that enables the other Police car to vault it.
Plot hole: How can a doctor (not a veterinarian) with no medical equipment tell for certain how far along a pregnant elephant is, especially when the gestation period for an elephant is 20-22 months?
Revealing mistake: When Mean Joe Green tips over Sheriff Justice's car, parts of the engine are missing.
Factual error: There is absolutely no way a Trans Am can tow the weight of a 9,000 lb elephant, plus the weight of a newborn elephant and 2 trailers. Such weight with a car like that would, at the very least, break an axle and destroy a transmission.