Bart's blackboard line, "My homework was not stolen by a one-armed man", is a reference to The Fugitive and Richard Kimble's saying that a one-armed man killed his wife.
The line has also been interpreted by some fans as referring to Herman Hermann.
At the bookstore, in order to cover up his and Marge's looking through the "Marital Relations" section, Homer accidentally grabs a photography book by Robert Mapplethorpe and screams when he gets a look at the contents (Mapplethorpe was famous for the homo-erotic nature of his work).
The book on tape, Mr. and Mrs. Erotic American by Paul Harvey, which Marge and Homer purchase, includes some of Harvey's broadcasting mannerisms such as beginning by saying "Hello, Americans" and ending by saying "Good day." (The voice for Harvey's reading was provided by Harry Shearer.)
Also in the bookstore, the fictional (as in non-existent) Al Gore books Rational Thinking, Reasonable Future (which Lisa mentions) and Sane Planning, Sensible Tomorrow (which she buys) are tongue-in-cheek references to Gore's real-life 1992 book, Earth in the Balance.
When Lisa buys Sane Planning, Sensible Tomorrow and Gore is notified as soon as the clerk scans it at the counter, the music in the background is very reminiscient of the X-Files theme.
The "X-Files-style" music also plays when Bart peers through his telescope at the adults (Revitalizing Tonic customers) arriving at their houses, hurrying inside, and closing the curtains.
When Al Gore is notified that someone has finally bought a copy of his book, he celebrates by putting on an LP record and playing "Celebration" by Kool & the Gang.
In the flashback of young Homer watching the televised presidential press conference, then President Kennedy addresses Helen. Helen Thomas was the first and at that time only female member of the White House press corps.
Lisa references Occam's Razor, a 14th-century theory still cited today as a counter to needlessly complicated explanations.
Milhouse's line "We're through the looking-glass here, people" is from the Oliver Stone movie JFK. The line is also a reference to the Lewis Carroll book Through the Looking-Glass and has become a slang term meaning to enter a world where nothing is as it appears — such as investigating behind-the-scenes goings-on.
When Grampa is selling his tonic, he's mostly seen dressed as a quintessential Southern Colonel, an image strongly associated with Colonel Sanders, the founder of KFC.
The man in the crowd in Spittle County who proclaims, "I'm not convinced. I've had bad luck with aphrodisiacs." is a parody of Ed Wynn.
When Homer leaves to 'do some serious thinking', he drives away from the house in the orange station wagon (Marge's car), but arrives at the farmhouse in his pink sedan.
When Homer and Marge are in the car, between scenes, the windscreen goes missing. It becomes noticeable when the mirror appears and disappears, and Abe's head manages to pop out when he and Homer argue over the getaway music.
In this episode, both Homer and Grampa set fire to the Simpson farm, and it burns to the ground. The later episode "E-I-E-I-(Annoyed Grunt)" creates a plot hole, as the Simpsons temporarily move to the Simpson farm. It could have been rebuilt.
Homer's shadow in front of the TV is still there even after 30 years. He could have been in the same position or it may just have been put there to 'show' how much time Homer spends watching TV.
Homer is shown shaving off his beard stubble, which grows back moments later. This gag was also done in "Some Enchanted Evening", where Homer has a clean shaven look for precisely seven seconds, then his stubble regrows.
In one scene in Bart's treehouse, Wendell's skin is yellow, rather than its usual white color.
