Bart's blackboard line, "My homework was not stolen by a one-armed man", is a reference to The Fugitive and Kimble's saying that a one-armed man killed his wife.
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).
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) may be tongue-in-cheek references to Gore's real-life 1992 book, Earth in the Balance.
As Homer and Grampa are escaping from the hillbilly crowd after a bad sales pitch, Foggy Mountain Breakdown is being played as "that getaway music".
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.
Among the rooms at the "Aphrodite Inn Fantasy Rooms and Conference Center" are the following:
The Arabian Nights Room
The Pharaoh's Chamber (Homer notes that it has a vibrating sarcophagus.)
The Caveman Room (Mayor Quimby, dressed in an "appropriate" outfit, comes out to say that the toilet is overflowing.)
The Safari Room
The Camelot Room
The Utility Room (the hotel's actual utility room; Homer and Marge end up here because everything else is booked.)
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, he later leaves the farmhouse in the orange station wagon again.
When Homer and Marge are in the car, between scenes, the windscreen goes missing. It becomes noticeable when the rearview 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-D'oh" creates a plot hole, as the Simpsons temporarily move to the Simpson farm, though it could have been rebuilt.
In one scene in Bart's treehouse, Wendell's skin is yellow, rather than its usual white color.