In the car-ramming scene, the 55 rams the right door of the Studebaker twice; when he pulls up to Rosalie the door isn't damaged.
In the car-ramming scene near the end, the hood ornaments repeatedly disappear and reappear between shots.
In the interior shots of the Studebaker just before Jonathan runs over the fire hydrant, the left rear window is partially open, but when the wreck is shown, the window is closed. we see the wreck, the window is closed; just after the wreck the front bumper is undamaged, but when he's driving home, it's badly bent.
In the fight scene at the drive-in, the menu on the wall lists 95-cent hamburgers--a bit steep for 1956 or even 1966.
When Marilyn is getting undressed, her necklace disappears after
she takes off her lower underwear and before she takes off her brassiere.
After Jonathan rams Kenny's car into the fire hydrant, he returns to the store where Rosalie works and asks her out. His car collapses in the front end; its hood is lower than Rosalee's apron. But when he drives away, the car's hood is higher than her apron.
When Kenny pulls into the gas station where Gene is working to pay off the repair bill on his father's car, the wing vent windows show signs of bubbling between the laminations. Since this movie was set in 1956, a 1955 automobile (the Chevy convertible) wouldn't show this result of the aging process. It's a phenomenon of safety glass that happens over several years of exposure to the elements. Also, there are no rubber window bumpers at the top of the driver and passenger side window tracks (directly behind the wing vent windows).
Many of the songs used, while true to the spirit of 1956, were actually released in later years.
As Kenny and his pals make their way into the drive-in, there is a 4-sided illuminated Kroger sign in the background that is not true to the era.
Before the final car chase, Jonathan is shown against a brick wall near the storefront. Right behind his head is at least one blue plastic masonry wall anchor. These weren't available in the 1950s.
The film is set in 1956, but Gene's motorcycle is a Triumph made in or after 1963; it uses a unit twin engine which was not made until 1963, and the style of badge on the gas tank was not used until 1969.
At about 48:42, Gene and Bunny are heading out of town on Gene's motorcycle, crossing the bridge that says "Nelsonville" while they are leaving town, with the sign eventually at their backs. In the next shot they're on a curving road with a nice view of the river on the right and they are coming toward the camera while they are leaving town. At the beginning of the movie Gene's moving truck makes its way into town, but they show the truck going in the same direction as Gene and Bunny were going on the motorcycle while they were leaving town.