Woody combs his feathers into the shape of a duck for a split second, a nod to a popular pompadour hairdo colloquially known as a Duck's rear end. Buzz, otoh, flattens his fashionable buzz cut flat top with a hammer.
The depiction of everyday high school life, including the sock hop and the drive in restaurant, is quite accurate for the time. The adolescent adventure theme was a common one that dates back to the days of Andy Hardy.
The house shown is futuristic mid century modern architecture, which was a popular emerging design trend during the postwar years.