Award Snub: The film wasn't nominated for Best Picture.
Despite having one of the biggest selling soundtracks of all time, none of the songs that The Bee Gees contributed were nominated for Best Song. Not "Stayin' Alive", not "Night Fever", not "How Deep Is Your Love?", not "Jive Talkin'", not "You Should Be Dancing", not "More Than a Woman", not "If I Can't Have You".
Awesome Music: There is a reason that the soundtrack album was certified 15x platinum. How awesome was the soundtrack? Alice Cooper remembers panning the album to fans and the public, but privately, thought it was (and still is) the best album he's ever listened to.
Broken Base: Stayin' Alive, the original film's much maligned 1983 sequel, is this in spades. Quite a bit of fans think of it as being So Bad, It's Good (olden Raspberry Award founder John Wilson's book The Official Razzie Movie Guide put it in the "100 Most Enjoyably Bad Movies Ever Made" list). Plenty of viewers can't stand it in the slightest (the sequel has a whopping zero score on Rotten Tomatoes).
Do Not Do This Cool Thing: Despite portraying Tony Manero's life as violent, shallow and ultimately pointless, the movie won Disco millions of new fans.
In possibly one of the strangest crossbred memes in Internet history, this film plays a major part in a Touhou meme: Travolta's pose from the poster is extremely similar to the pose taken by Nagae Iku when she declares a spellcard, and fans did the rest. The meme is so prolific that Danbooru, usually dedicated to anime, manga, and video games, has tags for Saturday Night Fever and John Travolta.
Narm Charm: A lot of Travolta's moves, which have been endlessly parodied, come off as ridiculous and are hard to take with a straight face, but they are really cool anyway and Tony Manero exudes an engaging charisma.