Revealing mistake: When Herbie is being pulled from the truck at Crazy Dave's, Herbie goes into reverse and the camera does a closeup shot of one of the rear wheels reversing. If you look carefully, you can see an extra set of small wheels behind the tyre which are obviously propping the car up enough so that the cars proper wheels will only skid and not get any traction.
Revealing mistake: When Herbie is getting unloaded from the truck in the beginning, he fights off the two guys by trying to go in reverse, but he squeals the tires. You can see the peel out tracks from previous takes when they show his tire.
Answer: Max is Lindsay Lohan - she doesn't want her dad to know she is racing so when she first has on the racing suit and helmet she says she is Max.