Wally's car is a 1953 Chevrolet 210 Convertible.
This is the final of six appearances Jess Kirkpatrick makes in the series, each time as a different character.
The textbook featured is Geometry by John Kaufman.
As Wally test 'drives' the car with Ward, [against a 'stock footage' background], the facade of The Elmiro movie theater in Santa Monica, CA is seen. It opened in 1934, and was in operation through the 1980s.
Beaver tells June it'll be "four years and 36 days" until he can drive. The age for a learner's permit was 17, as disclosed when Wally wanted to start driving. So at this point Beaver is 12, about to turn 13.