When Ward and Wally take a test drive it's clear the car doesn't have a windshield.
Ward, speaking to Wally about having a driver's license and insuring the car, says
"... it doesn't make any difference if you drive it around the block or drive it to California ..."
In Beaver's Doll Buggy (1961), Ward's 1961 Plymouth Fury is shown with a California license plate, though it does not resemble any plate issued by California.
When the Cleavers are going to dinner Wally nearly hits two pedestrians backing out of their driveway.