The home movies that Alan watches are actual home movies of Ben Savage as a young boy. The clips are from Ben's birthday (where he gets some WWF wrestling action figures), Christmas (where a very young Ben drives an electric Power Wheels toy car), and a soccer game where Ben looks at the camera as someone shouts his name. William Russ and Betsy Randle's voices dub over the actual dialog of presumably Ben's and Fred's parents.
The judge is played by Dan Lauria, who played Ben Savage's brother Fred's father on "The Wonder Years."
When Cory is trying to teach Morgan sports, she mistakenly calls a boxing glove a boxing mitten. This is precisely how Cory referred to his father's silver gloves (given as a gift) in Kid Gloves (1994).
Alan said he took Eric to the DMV on his 16th birthday because it's a Matthews men tradition, but in the season one episode, It's a Wonderful Night, Eric went with his friend, Jason, to the DMV, where he failed his road test. Although Alan possibly went with Eric the second time, he clearly states he went with Eric on his birthday & also showed no signs of anger when Eric went with Jason.
Topanga is older than Cory.