Factual Mistake In any scene where Llewyn is using a capo on his guitar, the capo he is using is a Shubb capo. They are excellent and he probably would have used one, save for the fact they were not invented until 1980, around eighteen years after the film takes place.
Factual Mistake In the scene where Llewyn is standing on the elevated train platform, a train comes in and it's one of the trains currently in use by the NYC subway system, not a train that was in use in 1961.
Continuity Near the beginning of the film, Llewyn goes into a subway station. The train that comes in is a different car model than the one he is sitting in in the next shot. Also, the exterior shot is of a train that did not yet exist in 1961. That model was introduced around 5-6 years later.
This film marks the second time Oscar Isaac and Carey Mulligan have played opposite each other. The first was in Drive where they played a husband and wife.
Loosely based on incidents in the life (and the 2005 memoir) of the late Dave Van Ronk and the Greenwich Village music scene in and around the real-life Gerde's Folk City club.
The Coen's usual choice for cinematographer, Roger Deakins, was unavailable as he was busy shooting Skyfall (2012).
The "Inside Llewyn Davis" album cover is based on the cover of the album "Inside Dave van Ronk".
Scott Avett of The Avett Brothers auditioned for the lead role of Llewyn Davis.
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