It is unknown why the Repo Depot was repossessing the merchandise of Karma-Ceuticals six months before bankruptcy. Although with the owner citing a crystal as a resource, there's a chance she had much less time
Homer accurately refers to the Bill of Rights as being part of the Constitution.
Marge's potential conclusions she writes down based on cell phone calls are:
The scene at the beginning of the episode, just before playing "Sing, Sing, Sing (With a Swing)", refers to several elements in 1939:
Franklin Delano Roosevelt being the president:
An ice cream cone costing only a nickel
Benny Goodman's new song (referring to "Sing, Sing, Sing (with a Swing)") hitting the charts
Not mentioned in the broadcast itself, but Homer references Adolf Hitler planning to start World War II when stating while panicking over seemingly traveling back to 1939 that he has to "warn everyone about Hitler"
When Lenny and Carl change the radio, the song playing is 1983's "The Safety Dance" by Men Without Hats; Bill and Marty's comment about them being known today as "Men Without Jobs" is a reference to "Safety Dance" being their only major hit, and the band being broken up at the time (although as of 2018 they have since reunited and still tour and record)
Other than those four, other exhibits seen include the Spirit of St. Louis, Lou Gehrig's jersey bat and ball, the Liberty Bell, the Space Capsule, Polly Doodle, a rocket, the US Flag dating back to the War of 1812, the 1911 high-wheeler automobile, the Don't Tread on Me flag of the Sons of Liberty, the statue of Paul Revere, and a cannon.
Lisa's favorite movie (at least until Homer recorded over the VHS tape) was Disney's The Little Mermaid.
Homer mistakes Lisa's favorite movie for 1968's "The Odd Couple", and poorly chants the iconic theme music
While inside the Karma-Ceuticals box, in order to alleviate boredom, Homer starts singing Art Blakey's The Witch Doctor. After Lisa's session inside the box was finished, a badly bruised Homer sung slightly modified lyrics to the above song where he requested for the Witch Doctor to run a cardio test, owing to the very chaotic events he had to endure in the box, such as being repossessed, unknowingly buried alive by the Flanders family, then going through an underground channel before eventually being redelivered to Karma-ceuticals by Chief Wiggum.
Bill and Marty mention the films Animal House and Terms of Enderment during their radio broadcast near the start of the episode ("This Place makes Animal House look like Terms of Endearment!"; Animal House being a comedy while Terms of Endearment is a drama).
When Lisa is looking at Abraham Lincoln's hat, the stars on the United States flag in the museum are blue instead of white.
At one frame in the kitchen when Homer is holding Maggie, the walls and hinges of the kitchen are colored pink instead of light purple.