In "Cleanliness is Next to Impossible," Oscar actually wants to change his slovenly ways because they bother his girlfriend, so Felix attempts to help him out with psychology by bringing in a hypnotist friend played by Allan Arbus, better known as army shrink Sidney Freedman on M*A*S*H.
One of the origin stories about the guys' friendship has Felix as a Rogue Juror, with Oscar having to room with him when he forces a sequester. Jack Klugman had starred in the classic film of this trope, 12 Angry Men.
The TV show featured a greatly increased focus on Oscar's gambling, especially at the track, and Felix's love of opera because those were particular interests of their respective actors.
Oscar's wardrobe on the show was, in many cases, Klugman's own.
Edited for Syndication: When Klugman and Randall complained about the laughtrack during the first season, ABC aired a trial episode without one (the episode in which Oscar gets fired from the paper and takes a job with a girly magazine). While initially syndicated without a track, one has been edited in in recent years.
Mainly focused around eliminating any hint, much less outright reference, to homosexuality. This is why the "Can two divorced men share an apartment without driving each other crazy?" spiel was added to the opening credits; it also resulted in one script being tossed out completely and the end of another ("The Flying Felix") being heavily rewritten.
Like it happened to The Brady Bunch, ABC's standards at the time still forbade as late as 1971 that divorced characters could have children. Oscar (who had two sons in the play and movie) became explicitly childless, while Felix's kids began appearing in the second season.
In the third season the network decided that what the show needed were guest stars. The show almost became a Lucy-like star-of-the-week clone, with everyone from Howard Cosell to Bob Hope to Bobby Riggs to Rodney Allen Rippy taking their turn at bat.
A rare live action example; in the film, one of Oscar's poker buddies is played by John Fiedler, who is instantly recognizable as being the voice of Piglet from Winnie the Pooh, as well as several other characters in Disney animated films from The Seventies. In the series he also played as the abusive owner of a Lassie-type collie in the episode "The Dog Story."
The Pigeon sisters Felix and Oscar dated in the film and the first season of the TV series also did the voices for the geese sisters, Abigail and Amelia, in The Aristocats, and Maid Marian and Lady Kluck.
Prop Recycling: The 'black donut' painting from the second season episode "Security Arms" shows up again in season three's "Take My Furnature, Please".
Husband and wife Jack Klugman and Brett Somers playing a divorced couple. In real life, Klugman and Somers split up during the series and she still came back to guest star, meaning they were a separated couple playing a divorced couple.
Klugman's son Adam appeared as "Little Oscar" in a few episodes.
In a later episode of the series, Penny Marshall's real life brother (Odd Couple producer Gary Marshall) and sister appear as her character's relatives, and her then-husband Rob Reiner played Sheldn, Myrna's boyfriend.
Un-Cancelled: The show had decent ratings through its inaugural season, but later plummeted, to the point it was cancelled in 1972, 1973 and 1974, only to be renewed by summer reruns, which got higher audiences than in their first runs.
Vindicated by Reruns: The show kept shifting timeslots while on the air, so only during summer reruns, when it was on at a consistent time, did it gain a significant audience. When the series finally ended and went into syndication, it got those consistent timeslots once again. Its popularity skyrocketed (just as Klugman himself had confidently predicted).
Art Carney (who played Felix on Broadway) wasn't seen as very marketable by Paramount, so Frank Sinatra, Dick Van Dyke and Tony Randall, among others, were considered for the movie role before settling on Jack Lemmon, while for the part of Oscar, Jackie Gleason, Mickey Rooney and Jack Klugman were among those considered before Walter Matthau was called to reprise his role.
For the TV version the characters were originally to be played by Dean Martin or Art Carney as Felix and Mickey Rooney or Martin Balsam as Oscar respectively.
Written-In Infirmity: Klugman and Randall took on the roles again in a series of potato chip commercials, all of which had to be written around Klugman's nearly non-existent voice after his heavy smoking resulted in him losing a vocal cord. Then a reunion movie was made, by which time Klugman had regained some volume, but still spoke in an extremely raspy and wheezy voice, so Oscar is said to have recently had a throat operation.