Continuity mistake: When the Wraith first shows at the drive in, Packard's car hood shows signs of the gunshots that the Wraith blows in his car, but that doesn't happen until a few minutes later in the film. (00:28:00)
Revealing mistake: The "blower" on the yellow Firebird never runs. NO wonder he couldn't beat the Wraith. (00:44:10)
Continuity mistake: During the chase scene where they attach the "engine killer" remote to the Dodge M4S (aka Wraith's vehicle), 2 Chevy Malibu Cop cars are barreling up the road towards the racers. Once the cops pass the starting line, the cars are now Dodge cop cars. (00:44:25)
Visible crew/equipment: In many of the racing scenes the camera crew's shadows can be seen at the bottom of the screen. (Corrected in the DVD version).
Revealing mistake: After Packard's car crashes with the Turbo Interceptor, his body is lying on the mangled car. If you look close enough you can see Packard's head moving slightly as if trying to hold still.
Other mistake: As Packard backs out of the cemetery there's no damage to his car, despite crashing through an iron fence and headstones.
Plot hole: Near the end of the movie, when Packard is about to race the Turbo, he puts on a helmet. Where exactly did he keep this helmet? The '77 Corvette is a two-seater with very little storage space for the passengers. Oggie and Minty's helmets could have been in the back seats of their cars.
Audio problem: When Oggie races the Turbo interceptor, the engine sounds for his car are from a V8, though his Chrysler Daytona is powered by a turbocharged 4-cylinder.
Revealing mistake: As the sheriff's car broadsides the car carrier, after the explosions, you can see the cars were junkers, set up to fall off the carrier.
Visible crew/equipment: After the Firebird crashes after racing from the cops, the Wraith turns around. As it does, the crew and equipment are reflected on the panels of the car.
Answer: After the first race where Augie is killed the sheriff says "I've been waiting to catch you guys in the act. Been waiting and watching." So we can assume there were complaints made however the sheriff may not have had enough evidence to shut them down completly. As far as the state police, I'm not sure. May be a jurisdictional thing.
Mister Ed
I agree with this answer. Packard was very careful not to flagrantly break any laws. He even said this to Loomis in the "paper doll" scene later in the movie - Packard says that the gang hadn't done anything except "bust the speed limit."