The alternate ending to "Who Shot Mr. Burns?" (featured in the 138th Episode Spectacular) was created to prevent any staff (be it writers, or even the overseas animators) on The Simpsons from spoiling the mystery. There were also many people who could have shot Mr. Burns as shown in the same episode. This included Apu (who would have fired multiple rounds instead of just one), Moe, Tito, Barney, and even Santa's Little Helper (who held the gun in his mouth and somehow pulled the trigger).
While scanning for the DNA, names like (Richard M.) Nixon, Gutentag (German for "good day"), (Mike) Tyson and (Colin) Powell can be read on the screen.
This episode is referenced in the American Dad! 100th episode, 100 A.D. where Roger comes in and says at the start "Tonight we shall find out who killed Mr. Burns", before being told that that happened fifteen years previous and that it was Maggie.
Burns' hospital room number is 2F20, which is the production code for the episode.
According to the DVD commentary, the contest that coincided with this episode actually had a false winner. No one had guessed that Maggie did it, and pressured by FOX to give the reward to someone, they chose an actual contestant who guessed that Smithers shot Mr. Burns.
There is another reference of Maggie as a "killer". In the episode "Poppa's Got a Brand New Badge", Homer is threatened to be killed by the mafia after stopping their business. Just as the mafia is about to kill Homer, Maggie shoots all the gangsters, wounding them. Marge and Homer later recall the events of this episode.
In The Cartridge Family, Marge also brings up the time Maggie shot Burns. However, Homer says that he thought it was Smithers, leading to Lisa's reply of making the case more likely.
In "The Old Man and the Lisa", Mr. Burns comes to the Simpsons house for Lisa, asking her to help him rebuild his fortune after he loses all his money. While in her house, Homer shows him Maggie, and she makes a gun shape with her hand. Mr. Burns then says "Oh yes, the baby who shot me."
The alternate ending (mentioned above) was featured in the 138th Episode Spectacular, along with several (fake) alternate versions of Burns getting shot, with a different culprit in each.
The "Outhouse Gag": Grampa abruptly ends a discussion to "use the outhouse." Lisa says that the family doesn't own an outhouse, which causes Homer to panic and run outside to try to stop Grandpa from befouling a building (Homer's toolshed) that only resembles an outhouse. The gag is later repeated in Bonfire of the Manatees.
Barney Gumble is the only one of the suspects who wasn't actually interviewed/cleared before Chief Wiggum scanned Maggie's eyelash.
Maggie's shooting of Mr. Burns, or more specifically, how she lured Burns over to be shot, was given a subtle reference in The Simpsons Bowling with Mr. Burns' victory screen, where Mr. Burns when attempting to take his trophy had Maggie pop out and then offer Mr. Burns a lollipop, only for Mr. Burns to proceed to beg for mercy before being knocked out by Maggie throwing the lollipop at him.
Grampa calls "Smithers" "Smingers".
The musical score that ends the Part one of the episode (when the credit rolls) is a parody of John Williams' Drummers' Salute, which is part of the musical score he wrote for Oliver Stone's movie JFK.
The scene where Chief Wiggum has a dream in which Lisa speaks backwards is an obvious homage to Twin Peaks and Special Agent Dale Cooper's interaction with The Man from Another Place and his hair upon waking up also references Cooper's hair after waking up from a similar dream. Also, after Homer escapes from the paddy wagon, the Squeaky-Voiced Teen speaks to his manageress Diane, which is the same name as the unseen secretary that Agent Cooper dictates messages to.
In the first part, Mr. Burns sings "hello lamppost, what you knowin', I'm come to watch your power flowin'", which is close to the lyrics of Simon & Garfunkel's '59th Street Bridge Song (Feelin' Groovy)'.
Sideshow Mel demonstrates deductive reasoning and logic similar to that demonstrated by noted fictional detective Sherlock Holmes. This connection is further noted by Mel's smoking of a pipe during his reflections, as Holmes was frequently known to do.
The opening sequence of Part Two, wherein Smithers dreams that he merely dreamed shooting Mr. Burns, before going on to dream that they are in fact undercover detectives on the 1960s Speedway racing circuit, is similar to an incidence on the 1980s soap opera Dallas, in which the events of an entire season (including an attempted murder) were explained away as being merely a character's dream which many fans hated.
Willie's interrogation scene where he is wearing a kilt and uncrosses his legs is a reference to Sharon Stone in Basic Instinct. Moe's lie detector test also alludes to the film.
"Speedway Squad In Color!" may have been a reference to the crime TV show "Police Squad In Color!"
Smithers mentions that he's not a catholic, but that he did attempt to march in the St. Patrick's Day parade, a reference to the previous policy of not allowing gay groups to march in St. Patrick's Day parades and the protests that often took place around them.
Realistically, Smithers would be still be arrested for shooting Jasper. Of course given the Springfield PD's unorthodox methods for handling different crimes that probably didn't occur to them. Either way, Smithers would've probably escaped severe punishment, as Jasper appeared to have no recollection of being shot, and thus presumably would not have pressed charges. Smithers also didn't wound Jasper, or cause him any harm.
The bullet claimed to be the one which shot Mr. Burns clearly cannot be such, as it is an UNFIRED bullet, with the shell still attached the slug. It's not the first time the crew has made this error.