Alternate Aesop Interpretation: Is the message about the fact that not many talented artists make it big or is it that self-destructive, foolish and unrealistic choices are what stop them from making it?
Ambiguously Bi: Was Mike Llewyn's partner or...partner? Certainly the depths of Llewyn's grief indicates it could have gone either way.
Award Snub: All but ignored at the Academy awards, despite being one of the best received movies of the year. Considering the immense competition present during that year, though, it might be a bit justified.
Ear Worm: Marcus Mumford and Oscar Isaac's rendition of Dink's Song.
Hilarious in Hindsight: In the film, Oscar Isaac and Adam Driver sing "Please Mr. Kennedy", a song where the narrator doesn't want to go to space. Two years later, they starred in Star Wars Episode VII: The Force Awakens. For bonus points, the CEO of Lucasfilm is Kathleen Kennedy (though a Mrs, not a Mr).
They also play protagonist (Isaac) and antagonist (Driver), for added delight if you're a fan of this film.
Jerkass Woobie: Despite Llewyn's unpleasant personality and antagonism towards seemingly everyone he knows, he is shown to regret many of his failings, and his lack of success or any good luck at all makes him quite sympathetic.
Narm Charm: "Please Mr. Kennedy" is a silly novelty song about manned space flight, featuring stuttering and quirky backing vocals. It is quite entertaining.
Tear Jerker: Llewyn's final rendition of "Fare Thee Well", sung with perhaps the most raw emotions he had shown throughout this movie. And can be interpreted that he has rather woefully moved on since his partner's death. It's a glimmer of light in such a Downer Ending.