Barney's accidental shooting and killing a woman crossing Evergreen Terrace was later referenced in the episode "Homer and Apu" (when Barney tips over the large bottle of Mrs. Butterworth and freaks out, yelling "It's all happening again!").
Homer's calendar has September with 31 days on it. September has only 30 days.
Coincidentally, Johnny Ramone died in 2004 on September 15th (which is the day established to be Mr. Burns' birthday).
Milhouse is implied to be missing (cf. the scene of Smithers overlaying pictures of Bobo with pictures of Milhouse on a milk carton).
Bobo was made with 100% cotton.
Smithers' birthday wish is to have Mr. Burns jump out of a cake and sing to him a la Marilyn Monroe.
The UK and Canadian airings of this episode edit out The Ramones' insulting language during their performance at Mr. Burns' party ("I'd just like to say this gig sucks," "Up yours, Springfield," and "Go to hell, you old bastard!" were the three lines edited).
Tommy Ramone, the last surviving original member, was dead in July 2014 due to cancer (although by this point he had been replaced by Marky, who is still alive and active in music. Also worth noting original bassist DeeDee (who died in 2002) had also left the band and was replaced by CJ Ramone, who is also still alive and active).
Notice the reuse of animation when Lisa says "I'd like to believe that this time" in dire hopes of Homer concealing his butt for good.
When the mob plans to give Bobo back to Maggie, Nick Riviera has brown hair instead of the usual black.
When Lenny and Carl observe the spinning cupcake holder, they are wearing polo shirts instead of their usual suspenders and sweater respectively.
Burns' Mansion front gate B is actually the number 13.
Mr. Burns mistakes The Ramones for The Rolling Stones, ordering Smithers to have the latter killed. As Mick Jagger (singer for The Rolling Stones) appears later in the series as a guest star, we can assume Smithers never had the order carried out.
The title of the episode is a direct reference to a reoccurring theme in the film.
The opening scene of the episode is also reference. Rosebud is the final word of the protagonist in the film, Charles Foster Kane. The scene where Burns throws snow globes on his bedroom's floor and a reflection of a shattered one where Smithers enters the room mirrors from the film, with a nurse entering the room of the late Kane - this is an exact reshoot of an infamous scene from the film.
The guards outside Burns' Mansion resemble the Winkie Guards from the classic 1939 movie, The Wizard of Oz They even sing a similar chant which is "All we own, we owe".
Initially, when covering up that he is lamenting his loss for Bobo the bear when Smithers questions who Bobo is when waking him up, Mr. Burns mentioned that he hated the fact that Sheriff Lobo was cancelled. Similarly, Homer Simpson has a nightmare relating to Sheriff Lobo before realizing in horror that the day is Burns' birthday.
Some of the photos of Mr. Burns at his birthday reference several things. One of him as the soldiers at Iwo Jima, one of him in a white dress that references Marilyn Monroe in "The Seven Year Itch" and an image of Muhammad Ali defeating Sonny Liston altered to have Mr. Burns's face on Muhammad Ali's body.
The Ramones appear, performing for Mr. Burns and then insult him.
Just before Smithers announces Homer Simpson's comedy act, he mentions that a dog resembling Lassie was run over in the parking lot, also unintentionally ruining Homer's comedy act.
The costume Homer Simpson wears during his comedy act, consisting of a blazer and wielding a golf club, are a reference to the outfit often worn by standup comedian Bob Hope.
After Burns is taken away from his family they remark that "At least we still have his brother George." George has an uncanny resemblance and mannerisms as comedian George Burns.
The scene where Mr. Burns walks in the room and says, Smithers, I'm home! is a reference to the show I Love Lucy.
Shows that Mr. Burns interrupted include a reference to Barney and Friends, Soul Mass Transit System (Soul Train), and Bumblebee Man.