Continuity mistake: During the sequence where Kowalski is being chased through the mining buildings, there's a shot where the passenger-side mirror gets knocked off the car by a jutting pole, and the camera tracks it to breaking on the ground. But the next shot showing that side of the car shows the mirror. It keeps appearing and vanishing for the rest of the scene (when it's not there, there's no sign of damage to the car: the car used for those shots appears to never have had a wing-mirror).
Factual error: At the end of the film, The Voice tells his radio audience the Challenger was estimated to have hit the bulldozers at 185 MPH. The top speed of the Challenger, with a 426 Hemi, was 145 MPH. A trained police officer (and there were many of them there), even estimating speed without a radar gun, would be able to estimate the speed much closer than that. It's part of their training to be able to make estimates that will hold up in court, and 185 MPH is noticeably different than 145 MPH.
Continuity mistake: The wheels on the Challenger when it bursts into flames are completely different than the wheels during the rest of the movie. During the movie, the wheels are factory Rally type wheels, and the wheels seen while the car is burning are aftermarket Cragar-type mag wheels.
Character mistake: When Gilmore radios for backup during the Monument Valley chase, he is told additional officers will join them in Blanding. Kowalski hears this on his scanner as they pass a sign saying Blanding is 14 miles away. Kowalski then stops dead in the road and turns around, and the troopers do the same, yet when Sgt. Preston grabs the shotgun, he justifies firing on Kowalski saying "We're coming on to Blanding!" In actual fact they would be heading away from Blanding.