Bart Gets an Elephant - S5-E17
Trivia: When Chief Wiggum is taking all the calls about the elephant and doesn't believe them, at the end of the last one he says 'Yeah right. And I'm Edward G Robinson'. Hank Azaria originally based Wiggum's voice off a bad impression of Edward G Robinson.
Homer's Barbershop Quartet - S5-E1
Trivia: During the episode, Skinner reveals that his POW number was 24601. This is the same as Sideshow Bob's inmate number and takes after the prisoner number of Jean Valjean in Les Misérables. That same prisoner number was also Hank Jennings' in "Twin Peaks".
Trivia: When homer lights his high school diploma on fire and starts singing the "I am so smart" song, when homer misspells smart, that was an actual mistake by Dan Castellaneta, who spelled it s-m-r-t instead of s-m-a-r-t, and then corrected himself.
Homer's Barbershop Quartet - S5-E1
Trivia: Some Beatles references in this Beatle mirroring episode: more obviously the rooftop concert, Abbey Road-esque second album cover, the Japanese Artist (Yoko) and the song Number 8 sounding like a dumbed down version of Revolution Nine. Probably less obviously is the closing line, 'I Hope We passed the audition' is the end of the rooftop concert and "Let It Be" album. On the back of the Be Sharps album is the four members in similar poses (hand positions and with Homer with his back to camera) to the inner sleeve of "Sgt. Pepper". The greeting at the JFK airport, their managers 'Boys, you've just recorded your first number one', mimicking George Martin on hearing "Please, Please Me", the cries of "Wiggum forever, Barney Never" echo the "Pete Best Forever, Ringo Never". The list goes on.and on.and on.
Trivia: The 'nerd' with the thick glasses is based on the show's creator, Matt Groening.
$pringfield (or How I Learned to Stop Worrying and Love Legalized Gambling) - S5-E10
Trivia: Towards the end, Mr. Burns starts becoming insane, growing long hair and long, claw-like fingernails and toenails, and becoming obsessed with germs. This just what happened to Howard Hughes, the eccentric billionaire who died in 1976. Burns also has a plane called the "Spruce Moose." Hughes' plane was the "Spruce Goose," currently displayed in Long Beach, California.
Homer's Barbershop Quartet - S5-E1
Trivia: The reason the name 'The B Sharps' is so funny (at least to a musician) is that in music there is a natural half step from B to C. This makes a B sharp the same as a C natural. It is almost never referred to as "B sharp", but instead as simply "C".
Homer's Barbershop Quartet - S5-E1
Trivia: This is the only episode in which Homer is voiced by someone other than Dan Castellaneta; his singing voice is done by a member of the Dapper Dans.
Cape Feare - S5-E2
Trivia: Bob's prison number is A113. This number is often used as by alumni of California Institute of the Arts (most famously by Brad Bird, in his Pixar films and episodes of the Simpsons he was involved in, such as this one) - it's the number of one of the classrooms.
Tree House of Horror IV: The Simpson's Halloween Special IV - S5-E5
Trivia: When Marge asks Bart to explain how scary the episode is, she mentions the "War of the Worlds" broadcast on NPR. Narrated by Orson Welles, that radio serial was so chilling, a number of listeners actually believed Earth was under attack.
Cape Feare - S5-E2
Trivia: The gag of Sideshow Bob stepping on the rakes was only supposed to be him stepping on a single rake one time. But the episode's running time was short, so the sequence was extended as a time filler.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.