Homer still has his gun from "The Cartridge Family" in his sector drawer at the power plant, despite that Marge slipped it in her purse after realizing that she looked good with it (unless that's another gun that Homer bought that the family doesn't know about, or that Homer found out about the hypocrisy and chose to conceal it in his work station or this episode takes place during the aforementioned episode and Homer was bringing his gun to work).
Homer going through a range of different emotions after thinking that Mr. Burns woke him up at work is similar to how he went through the five stages of grief in "One Fish, Two Fish, Blowfish, Blue Fish."
"Dumbbell Indemnity" - Moe has to travel by bus (or taxi instead) because his car is unavailable. He asked Homer to ruin it due to insurance.
"The Homer They Fall" - Homer's relative imperviousness to his head being closed on by a drawbridge and driven on by a few cars can be explained by his incredibly thick skull covering which was revealed in this episode.
The title of the episode is based on the sign "Lost our lease!"
The melody played by the orb is very similar to that played by the music box in the film The Gate II.
On their way out of the museum, Homer tries to whistle to the music box, but Lisa tells him that he ended up whistling the Old Spice jingle.
The artwork Homer and Lisa climb to enter the museum is in the style of Alexander Calder, combining his early "Mobile" work with his later monumental phase, dubbed "Stabile" - even though Calder never combined the two.
Lisa said before that she should not have took the bus, but, in past episodes, she has been known to go to places by herself, like in Lisa the Simpson, when Marge says Lisa has been gone for hours, and she used the bus. (There is no proof, but it would make sense for her to do that.)
You can hear Homer's voice in the bar, but then he is sleeping at the Plant.
The blue and yellow on Homer's Ancient Egyptian headdress switch position with each other a few times.
How did Bart and Milhouse get past security at the plant? Everyone at the plant is incompetent.