The scene where Kermit the Frog graduates from college was filmed at Vassar College in New York. Director Frank Oz wanted it shot in front of the most academic looking building on the campus: the dining hall.
Rizzo the Rat appeared throughout the final season of The Muppet Show (1976) and along with Scooter as the Happiness Hotel bellhops in The Great Muppet Caper (1981), but this is his first major role with The Muppets and his first appearance with his more "wiseguy" personality.
Kermit should have known Miss Piggy wasn't going far - the train she leaves on is the Erie Lackawanna Railroad which was a local railroad servicing only New Jersey. Erie Lackawanna shut down in 1983 when it was taken over by New Jersey Transit Corporation.