The title is a reference to the Dallas plot, “Who Shot J.R.?”
According to the DVD commentary for this episode, a college kid found out the shooter just a few hours after the show aired and posted his results on the web. The staff couldn't give him the prize in the "Who Shot Mr. Burns?" contest because he didn't enter properly. They were going to send him something, but they couldn't find his online user name anymore.
This is the first time a character shouts out a swear word in front of Ned Flanders which is unknown to the audience. It again happened in You Kent Always Say What You Want.
Moe was given his surname, Syzlak, in this episode and it was chosen in order to make him a stronger suspect. When Burns falls at the sundial pointing to W and S, it can be interpreted as M and S. According to the DVD commentary, the name "Syzlak" came from a phone book.
This episode shows that Jimbo has concern for other people, this is seen when Mr. Burns is about to collapse after being shot from someone (which turns out to be Maggie) and Jimbo asks Mr. Burns if he is okay.
Dr. Hibbert's line "Well I couldn't possibly solve this mystery" is a reference to the short-lived The Cosby Mysteries that was airing on NBC at the time.
The music during the end credits is an homage to John Williams' score to JFK, specifically the cue "Drummers's Salute".
At the end of the closing credits of the episode, the Gracie Films logo sequence ends with a gunshot sound, referring to the very mysterious atmosphere of the episode.
Mr. Burns not knowing Homer's name.
There is a reference to the Simon and Garfunkel song "The 59th Street Bridge Song (Feeling Groovy)". After blocking out the sun, Mr Burn dances and sings "Hello Lamppost, Wat cha Knowing? I've come to watch your power flowing." This is a parody of the original lyrics with "Hello Lamppost, Wat cha Knowing? I've come to watch your flowers growing."
It's impossible for Marge to head back into the car to pick up Maggie and go straight to the sundial shortly after Mr. Burns collapsed unconscious on it.
When Krusty is in the crowd shots at the end of the episode, he inexplicably looks identical to Homer dressed as him. This is possibly due to the animators drawing Homer into the scene but then being reminded by the script that he cannot be in the crowd shots. This goof led to a theory that Homer was intending to shoot Mr. Burns while disguised as Krusty, but forgetting to remove his disguise when the real Krusty announces his return from vacation, thus appearing in the crowd shots.