In race 2, after Luke takes out the Russian, he reverses the car back up the track before spinning round to face the right direction, there is a van visible on the right hand side with the camera mounted on the roof on a boom.
After the initial chase in the yellow Mustang that ends with the hand grenades, in the shot with the police cars on they're roofs, as Luke says "get out" to the robbers, you see the crew on the left, some of them with fire-extinguishers running for the flames after the stunt. Also the boom-camera is visible.
During the bank robbery, just after Luke beats the two officers with the baton, a cameraman can be seen standing on the right side of the balcony behind Luke. The cameraman disappears in the shot showing the balcony (immediately after Luke picks up one of the officer's guns) and reappears in the next shot showing the balcony.
Just prior to the initial race the mass of prisoners are gathered and then released to run and fight their way to become a driver of the few cars available, on a first-come-first-race basis. Next, as they head down the track, the television production displays driver biography graphics with each of the convicts already posing beside the vehicle they just randomly acquired moments ago.
After the fight between Lucas and Big Bill, at the end of the riot, Lucas points a flame thrower at Big Bill then "kicks' him in the face to knock him out, which obviously misses Bill by at least 12 inches. Lucas then drops to his knees and puts his hands behind his head in surrender to the guards. As he does this, directly behind him are two prisoners fighting; one of them reacts to punches far wide of the mark as well.
The goof items below may give away important plot points.
Near the end of the film, when Lucas crashes through the garage door being chased by the missile, you can see that both rotary machine guns have been torn off the hood of the car. In the next scene they show him being hit by the missile and him exploding. The machine guns are magically right back where they were.