Continuity mistake: Towards the back end of the film, the lady arrives in her car, parks it at the side of the road and she is shot a few minutes later. Her car is seen at the edge of the road behind the sheriff's car when the boy runs down the road after breaking out, but her car has vanished when he drives the cop car away 30 seconds later. Also in the same scene of driving away, the sheriff's car has moved well off the road too.
Continuity mistake: When Kevin Bacon is shouting "did you open the trunk?" at the boys through the window of the sheriff's car, his hand is full palm on the glass from the exterior shots, but in an entirely different position in the shots of him from inside the car.
Factual error: At multiple points in the film, the Sheriff misleads the police dispatcher regarding his location. The Sheriff also laughingly dismisses any question of a stolen police cruiser, and the dispatcher just accepts it. However, police cars were universally outfitted with GPS tracking devices over 20 years ago, so the dispatcher should have been able to locate the Sheriff's cruiser and any other police cruiser in a matter of seconds without any radio verification whatsoever.
Revealing mistake: Throughout the movie, we are reminded repeatedly that Harrison and Travis are naive 9-year-old boys who have absolutely no knowledge of guns or gun safety. Near the end, when the two boys are trapped in the backseat of the cop car, they clumsily try to blow out the window with a 40 caliber semi-auto handgun, but they can't even figure out the safety mechanism. When they do release the safety moments later, young Travis suddenly takes aim and fires with a perfect two-handed forward presentation. We see the gun and Travis's hands in close-up, and he's properly holding the semi-auto with trained dexterity just before it fires. This appears to be a skilled stand-in firing the gun.
Factual error: The Sheriff clears all other police traffic on a specific radio frequency so that he can "secretly" chat with the two young boys. Of course, secrecy is crucial to the Sheriff's motivation all throughout the movie. However, police radios have extraordinary range, and police radio channels are constantly monitored by neighboring police forces, by other first-responder agencies, by civilian police scanners, and even by the news media. The Sheriff should surely know that it is impossible to conduct a "secret" or even "private" conversation over police radio.
Visible crew/equipment: When the boys approach the cop car and are trying the doors, the camera crane can be seen reflected off the bodywork of the car.