Larry King introduced himself as the moderator for the mayoral debate. However, that same debate has Birch Barlow asking the only 2 questions we see.
Bob's cronies stick two badges on Bart's shirt while in the limousine, but after they throw him out the badges are gone.
After the trial Bart smiles with teeth showing and a camera flash goes off. The subsequent newspaper photo shows Bart without teeth showing.
The plot hinges on a supposed act of voter fraud, and the evidence given is that Bob's campaign used the names of dead people and pets to vote for him. However, the polls showed 99 or 100% support for Bob anyway. So obviously, all the legitimate voters did actually vote for him, which means that the fraudulent votes did not make any difference. Bob really did win the election legitimately.
In the United States, mayors don't have the authority to pardon state level crimes like attempted murder - only governors do.
When Bart throws his radio out the window, there is still sound coming from the speaker, even though it's clearly unplugged. Bart's radio is presumably portable given that it has a handle, and these radios can often run on battery and automatically switch when unplugged.
Buddy Holly, Richie Valens, and the Big Bopper died in a plane crash together, but they are not buried in the same cemetery together. Additionally, Buddy Holly's actual grave spells his name as "Buddy Holley," which was his family's actual name.
Kent Brockman says "Mayor" Sideshow Bob was preparing to make a victory speech. Bob's title would actually be Mayor-Elect, since he hasn't been officially sworn in yet.