In keeping with the mystery of which state Springfield is in, this episode gives misleading clues. The map shown during the essay reading montage shows Springfield's state as being NT. The junk mail Homer receives shows the state as TA, and an enigmatic 6-digit zip code of 192005.
In the office of the congressman from Springfield's state, there is a State Seal. It depicts an ear of corn, a star, a beaver and a nuclear power symbol.
The eagle lands on the branch and holds an olive branch and arrow in its claws just like on the US seal.
The piano-playing satirist at the end of the episode is a reference to Mark Russell and Tom Lehrer. The song "The Deficit Rag" is very similar to Lehrer's "The Vatican Rag".
The woman's suffrage display Lisa visits is likely a parody of Susan B. Anthony. When Lisa mentions "she later appeared on the highly unpopular 75¢ piece" this is a reference to the Susan Anthony dollar coins, which were often mistaken for quarters by vending machines and cashiers.
The banner that reads "Brevity is... wit" is a reference to a line in Hamlet where Polonius says: "brevity is the soul of wit". The joke is that the banner is applying greater wit by increasing the brevity of the original Shakespeare line. Even funnier, as noted in the banner, the event is sponsored by "Reading Digest", an allusion to Reader's Digest, which abridges popular books for its readers.
During the White House tour, the Simpsons see a sign reading "On this spot, Richard Nixon bowled back-to-back 300 games," which Homer scoffs at. In real life, Nixon was an avid bowler; he even frequently bowled while he was President, finding that bowling fit well into his work schedule. However, it's unlikely that he ever bowled back-to-back 300 games. Ironically, Homer bowled a 300 game in "Hello Gutter, Hello Fadder".
Then-President George H. W. Bush is featured briefly in this episode, and is portrayed in a positive, albeit hokey, light. Shortly after this episode aired, Bush disparaged The Simpsons in a speech. Thus, Bush appears in four later episodes (one of which is the season seven episode "Two Bad Neighbors") in a much more negative light.
In the first shot where she appears, Faith Crowley's lipstick repeatedly changes color between pink and red.
When the Simpsons clap after the winner of the contest is announced, Maggie's bow disappears for a few frames.