A "Lassie"-like theme plays as Bart goes out to look for Stampy.
Bart's insistence that he wants the elephant as his prize (for winning a radio call-in contest) instead of the cash prize, and the resulting outcry continuing until his demand is met is similar to an incident on the 1950s "The Price is Right" (where a contestant made similar demands after being shown an elephant as his "bonus" prize, then being debriefed about the actual prize of cash)
Homer reads about this show in an old TV guide and remenices about it.
When the car hits a deer, the dialogue that follows references a song in this film.
An ivory collector named "Blackheart" tries to buy Stampy from Bart.
Stampy the elephant makes a reapperance
When Patty and Selma are seen on rocking chairs flying in the tornado
When Marge first sees Stampy through the window his eye spoofs the T-Rex outside the Jeep window