It opens with a shot of a microphone. It's 1961. Would a folk cellar like The Gaslight have had one? Or had need of one?
He goes round to his girlfriend's apartment and she has what looks like a hundred albums. In 1961 young people didn't have a hundred albums.
Somebody sings "The Last Thing On My Mind", which Tom Paxton didn't record until 1964.
The language is completely 21st century. In 1961 nobody came out with a torrent of profanity and if they did it certainly wasn't in front of women and children.
All that said, this is a haunting film. I'd happily watch it again tomorrow.
Would-be folk star Llewyn Davis is so consumed by the needs of his own career that the needs of the people around him simply don't seem real to him; plus he's so convinced of his own talent that he can't understand why anybody else should have the tiniest share of the spotlight. He thinks it's the managers and agents preventing him from being successful. He doesn't understand his real problem is people don't like him.
He gets to play a song for the Albert Grossman figure. The man listens to the whole song (every song throughout the film is given a complete performance), then looks at him and says the six words which everybody in the music business thinks and hardly anybody ever says: "I don't see any money here".