This episode title references Baby, It's Cold Outside
The song sung by the Simpson family while in the car is "Baby Shark".
The now-defunct Gimbels department 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.
Also in The Mansion Family he mentions that cause of his parents' death is: 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.