Vance changes the tire on the Thunderbird and doesn't ever remove the fender skirt. On that car, the fender skirt has to come off before all the lug nuts would be accessible. Even if the car was in neutral so that the rear wheels could be rotated, the wheel would be very hard to remove and replace with the fender skirt in place.
Although the rock 'n' roll music on the diner's jukebox adds to the rebel atmosphere of the film, diners in the 1959 time frame would more than likely have family friendly selections by Bobby Darren, Paul Anka, and Connie Francis. And in the south, mostly country music.
After visiting the liquor store, Vance downs a pint of Thunderbird wine and throws the empty bottle out of the car. The sound of the glass breaking on the pavement is heard while the bottle is still in the air.
The owner of the garage asks the gang who the NASCAR rookie points leader is. He then states it is Lee Petty. But seeing as this film is set in 1959 as per the September 1959 issue of Stag magazine in the garage and the 1960 Corvette, the correct answer is Richard Petty, Lee's son.