Gene's motorcycle is a Triumph made in 1963 or later. It uses a unit twin engine which was not made till 1963. The style of badge on the gas tank was not used till 1969. The movie was set in the mid fifties.
In the interior shots of the Studebaker just before Jonathan runs over the fire hydrant, the left rear window is partially open, but when we see the wreck, the window is closed. Just after the wreck, the front bumper is undamaged. When he is driving home in the next scene, the bumper is badly bent.
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).