Other mistake: Lightning Mcqueen is trying to become the first rookie in Piston Cup history to win the Piston Cup, but Doc Hudson won the Piston Cup in 1951 the first year that Hudson Hornets were produced, which also would have made him a rookie.
Continuity mistake: In the tractor tipping scene, Mater demonstrates to McQueen how to do it using two tractors before Mcqueen's first try. And then when McQueen accelerates to make the noise and we have a wide open shot of the field, we can see that all the tractors in the field are still turning. Missing are the two already done by Mater. (00:55:40 - 00:56:25)
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.
Easter egg: On the original "Cars" DVD, let the menu animation run twice. On the second time a Dinoco logo will appear for a few seconds. Quickly get to it and press select or enter. You will be greeted with a modified version of Boundin', used to test the animation for Cars.