A song "We Love You, Matlock" is a parody of song "We Love You, Conrad" by Bye Bye Birdie.
The giant floor piano in the store as well as Homer playing is likely a reference to the 1988 film Big which also features a similar scene and has Tom Hanks's character playing it too.
Also, when Homer first uses the giant-sized piano, its shown playing "Rock around the Clock Tonight."
The main plot of the episode is a reference to several controversies to Barbie, more directly the "Math is Hard" talking Barbie controversy.
The girl whose Stacy doll says Spider-Man quotes is based on actual events. Feminist activists calling themselves the "Barbie Liberation Organization" were replacing Talking Barbie's sound chip with ones from ToyBiz's Marvel Super Heroes figures and placing them back on store shelves.
While Abe Simpson is going through his elderly citizen complaints on the way back to the Simpson House (and promptly driving his family to immediately avoid him upon returning), one of the things he complained about was "The president is a Demmycrat." At the time the episode aired, Bill Clinton, who indeed adhered to the Democrat party, had been the President.
Malibu Stacy is referred to as "America's favorite eight and a half incher."
A sign in front of the factory reads: "PetroChem Petrochemical Corporation, Proud Makers of Caustic Polypropylene and Malibu Stacy".
Maggie can write her name on an Etch-A-Sketch, once again indicating her intelligence.
Stacy Lovell's ex-husband, Joe, has a line on his neck, like a doll.
It's revealed that Smithers owns the largest Malibu Stacy collection in Springfield, and was implied to be a frequent guest at StacyCon.
Homer plays the Simpsons theme song on the floor piano at the end.
Ironically, Krusty's gaffe during the voice recording studio (where he breezes through several lines and leaves before the recording even started) would be repeated during the development of the game Kingdom Hearts 358/2 Days where Christopher Lee ended up delivering his line as Ansem the Wise and leaving in a similar manner to Krusty (although unlike Krusty who did it largely out of arrogance, Christopher Lee did it due to having a very busy schedule that forced him to rush things).
When the Simpson family is about to leave for the mall, Marge's necklace changes from red to white while on-screen.
Abe can somehow reach the carhorn despite claiming that he can't unbuckle his seatbelt.
When the girls joke that Lisa said a dirty word, Nina's mouth did not move even though she clearly appeared to be speaking to Janey.
The speaker outside of Stacy's mansion changes depending on the angle of the shot. At first, it has lines going diagonally both ways, but then it only has horizontal lines.