During the final race when they take off, Billy's right tail light is out. In the next shot of the back of the cars, it's on. When they cross the finish line, there are a few frames you can see it's out again.
When Billy's Chevelle crashes into the bulldozer it switches from a 1969 model to a 1968 model (1968 GM A-body hardtops and convertibles have a vent wing glass assembly; 1969 model door glass is a one piece assembly)
The newspaper article that Billy leaves in Joe Garrett's mailbox has a headline which reads, "Iceman Eludes Police - Manslaughter Charged," implying that the article is about an incident from Garrett's past. However, the text of the article is actually about state laws identifying rape victims in court.
The tarantula that Garrett pulls out of the mailbox is quite clearly not the same tarantula that Billy put there.
A stuntman, not Brad Pitt, was visible making the U-turn next to Joe's patrol car.
Every time Brad Pitts character "Billy" cranks the volume of his car radio for a race, he spins the tuning knob instead of the volume knob.