We finally found out why Theodore was nick named "Beaver". It was because when Wally was little, he couldn't say "Theodore".
This final episode of Leave it to Beaver goes down in television history as the first traditional TV "series finale" (by today's standards) by ending with this "clip show." No other series prior to this had a special ending episode produced (with the exception of "Howdy Doody" in 1960--but it didn't use flashbacks and was not a sitcom!), they all just simply ended with a general story line that could have come at any point in the series.
Gilbert is in the class of '63
Gilbert Bates' middle name is revealed to be Grover.
The shadows of production personnel are visible in one of the golf course scenes when Mr. Langley walks toward the camera.
After the game they attempt to push-start Wally's car, but in other episodes it appeared that Wally's car is an automatic, making a push-start impossible.
Fred Rutherford's license plate number, which the property owner writes down, is WJG 865. The exact same license number is on Ward Cleaver's car in the Season 6 opening credits.
Since Wally and Ward come home together in Wally's new car, it's unclear what car the two of them had been using to travel from place to place while car shopping.