Other mistake: At the start of the film when the commentators are explaining the tie situation between the 3 cars the green arrow to the car is out of alignment and misses the car, instead pointing at the track.
Suggested correction: Pixar Creative Director, Jay Ward, who is this film's team manager (as well as art coordinator) has stated that this was deliberately done as a joke, for fun. Chick Hicks' green arrow does not line up with Chick Hicks. That it's a little bit off, in the same way that Chick Hicks is a little bit off. This is the video with Jay Ward explaining: https://youtu.be/ZkJre-eC-zE?t=25.
Trivia: The car crash suffered by The King in the last race is very similar to the accident that Richard Petty had in 1970.
Suggested correction: The ending crash has no similarities with Richard Petty's crash in 1970 at Darlington. The King's car didn't hit a wall. It most likely took inspiration from Richard's 1988 crash at Daytona.
Continuity mistake: After the first race, McQueen blew out both back tires. When interviewed after the race, his pit crew changes his rims with new tires, but the old rims have tires on them. They should be only rims, since earlier in the race we see him riding "on the rims" only, with sparks flying from the metal touching the track.
Suggested correction: McQueen's pit crew fixed his tires before the camera shot on him.
I think you missed the point of the mistake. 2 crew members are taking off both of McQueen's driver side tires (we can assume they replaced the passenger side off camera). But one should just be the rim. You're suggesting the pit crew replaced his tires off camera and then decided to replace his tires again when on camera.
Continuity mistake: Before Lightning falls off the end of Mack's trailer, you can see Snot Rod and one of the other cars running alongside the trailer. But when the camera moves to show Lightning coming off the trailer, you can see alongside the trailer in the background, and the cars are now missing. Camera switches back to the front of Mack, and the cars are back alongside again.
Suggested correction: Actually, they are still there. They're just out of view.
Corrected entry: In the scene where Doc Hudson is trying to give Lightning advice on turning on dirt he says "I'll make it simple, if you turn hard enough left, you'll find yourself going right" and his tires turn accordingly. For the rest of the scene, Lightning uses the reverse, saying "turn right to go left", including into the next scene where he is back pullie Bessie. For the most part there are no right turns in oval track racing.
Correction: No, there are generally no right turns in racing, but what doc is talking about is countersteering. Motorcycle and bicycle riders countersteer intuitively, but in a car, it is a learned action. With auto racing, countersteering sets up the car into an oversteer condition, pushing the tail out, and the driver must turn into the skid to allow the car to corner faster than not using oversteer. Thus the phrase "turn right to go left" makes sense. The tail is out after initially turning left, and in order not to spin, the car has to steer to the right, into the skid, to keep a controlled line through the course.
Correction: I think Doc is commenting on his mistake. Look at the way Lightning turns the first time. He turns the wheels left sharply and skids off to the right. McQueen has deduced that he should do the opposite.