The song sung by the Simpson family while in the car is "Baby Shark".
The now-defunct Gimbel'sdepartment store chain is shown and mentioned in the flashback scene from Mr. Burns's childhood.
Both NCIS: New Orleans and Quantum Leap are referenced when Wiggum talks with a justifiably irate Scott Bakula upon releasing him from custody. Similarly, Steve Ballmer references Mistaken Identity when being released. Sandra Bullock also puts on a blue blindfold when being released, referencing her role in the film Bird Box.
The Simpsons watch the "Fox News Yule Log", a parody of the WPIX Yule Log that ran from 1966 to 1989, and revived in 2001. This show features various "liberal" items being burned in a fireplace, including the U.S. Constuitution, the Bill of Rights, a portrait of President John F. Kennedy, and copies of The Origin of Species by Charles Darwin, It Takes a Village by Hilary Clinton, Silent Spring by Rachel Carson, and Emily Post's Book of Etiquette.
The life goals Sideshow Bob had were of the following:
Work till age 67
Retire with pension
Date age-appropriate woman
Find birth father
Mr. Burns says that both his parents died when he was little but in "Homer the Smithers" we see that Mrs. Burns is still alive at age of 122.
Also in The Mansion Family he mentions that cause of his parents' death is because they got in his way. If he ran over them then he would already be a grown man not a child because it is very unlikely that he would drive a car as being a child.
Also in "Rosebud" the flashback shows that he abandoned his parents when he was a kid along with his brother George and his teddy bear Bobo to live with a billionaire.
The flashback takes place in 1935 and in it, Mr. Burns is a child, but in "Monty Burns' Fleeing Circus" we see a flashback from 1906 and it shows Mr. Burns as a child, so after 29 years Burns wouldn't have been a child anymore.
The website that Lenny uses to buy his Christmas gifts doesn't have a top-level domain in its URL.
Homer's address on his Kris Kringle Union card lists him as living at Springfield Beach, which the same place Sideshow Bob's card says.