Deleted Scene: A scene that never made it beyond the script had Dr. Hibbert remove the bullet from Mr. Burns to help Chief Wiggum's investigation. In the actual episode, the episode skips straight to Wiggum already having collected the bullet.
Several fake alternate endings were created to keep the real ending secret. These endings were eventually shown in "The Simpsons' 138th Episode Spectacular".
Edited for Syndication: It removes the revelation of Abe getting back his Smith and Wesson, leaving the shot of the dug-up hole in the Simpsons' backyard in Part 1 unresolved. Both of Dr. Colossus' appearances are also edited out: the first, when Smithers says that Burns crossed over into cartoon super-villainy when he tried to block out the sun, and the second when Mel and Krusty attempt to explain to Wiggum that he's arrested the wrong man. There's a scene at the beginning where a group of rioters tear down the sun-blocking device (and rejoice when they learn it fell on rival town Shelbyville). It also trims out the part where Homer yells "BERSERK IS RIGHT!! May I have some iced tea, please?" Finally, when Lisa says, "Then, with your last ounce of strength, you pointed to "W" and "S", or from your point of view, "M" and "S," the part where she says "Maggie Simpson" afterwards is trimmed, and it goes straight to Mr. Burns saying he used his last ounce of strength to suck out his gold fillings and swallowed them.
Foiler Footage: Even though only a few of them could have been guilty, there was a gunshot, and Principal Skinner's gun had a silencer; Moe had a shotgun, which would've killed Burns, and Apu is shown using an automatic weapon that still leaves just one wound. They also recorded and animated a full alternate summation where Smithers goes through his whole Motive Rant, and it's explained how all the clues could have added up to Smithers being the culprit. As Troy McClure points out in "The Simpsons 138th Episode Spectacular", the DNA evidence has to be ignored for this alternate ending to work. There were also some shorter alternate endings which just depicted various (and increasingly unlikely) Springfieldians shooting Burns. The producers intended to leak the fake endings to media outlets, but could not find any that would take the bait.
The Season 7 Director's Commentary on Part 2 has them stating that originally Barney was going to be the shooter and end up in jail at the end, due to them feeling that they'd run out of material for him, but eventually decided on Maggie instead for comedy purposes. This could've been Foreshadowing, given that he was the only one not questioned by the police. Mr Burns even says "Take that Bowlarama" at one point - Barney once owned the Bowlarama.
There was going to be more evidence for and against other characters, including Barney, Apu, and even Jimbo Jones, but time ran short.
General Trivia
A viewer competition to guess the identity of the killer was held, but contrary to popular belief, the prize on offer was not a Contest Winner Cameo, but an illustration of the winner with the Simpson family. (The popular belief likely arose because of misleading promotional material for the competition that was phrased in such a way to imply the winner would appear on the show.) Due to contest regulations, a winner then had to be selected out of a random sample of entries, but nobody in the sample guessed the right answer. A random person from the sample was then selected as the winner, but the entrant who was chosen did not watch The Simpsons, so she decided to be paid a cash prize in lieu of being animated. However, one single viewer (who was not amongst the contest entries) correctly followed the episode's trail of evidence and concluded that Maggie did the deed; but when the producers tried contacting them, it turned out the email address was a college email address that was no longer in use.
had Dr. Hibbert remove the bullet from Mr. Burns to help Chief Wiggum's investigation. In the actual episode, the episode skips straight to Wiggum already having collected the bullet.