Bizarro Episode: The writers really ratcheted up the wackiness for this episode, which some viewers back then found to be out of character for the show. On the DVD Commentary, they said it was the last episode for the original writing staff, so they just gave up on making the show down-to-earth and went nuts.
Fridge Logic: How could Sideshow Bob flat out announce (over loudspeaker, no less) that everyone but Bart won't be killed by him and get away with it? Also, he didn't mention the Flanders kids being exempt from being murdered. Does he not know that Ned and Maude have children or is he going to get them next?
Perhaps Rod and Todd did something mean to Bob that we never heard about?
Homer requests to be John Elway in the witness protection program, despite being quite displeased at being made the owner of the Denver Broncos later in the series. Well, he imagined himself as the reason Denver lost to San Francisco by 56-7 instead of 56-0.
Also, the cigar Homer was smoking when the Simpsons first met Sideshow Bob in the episode was from Knoxville's World Fair.
At Sideshow Bob's parole hearing, the parole board fails to take into account overwhelming evidence that he had sent threatening letters to Bart (including several written in his own blood) and are so stupid to realize that "DIE BART DIE" is not a German translation.
Bob, after binding and gagging Bart's family, finally corners him on the houseboat. Instead of simply using his knife to brutally kill Bart and make his getaway, Bob arrogantly asks him if he has any last requests. Bart uses this opening to get him to sing the entire score of H.M.S. Pinafore. Bob complies and the score is long enough to give the pilotless, drifting houseboat to run aground, knock Bob of the boat and stun him long enough for the authorities to arrest him.