Ewan MacColl's The Shoals of Herring was composed for and first broadcasted in a BBC 'Radio Ballad' in August 1960. Since the film is set in 1961, Llewyn Davis could not have recorded this as an eight year old.
Llewyn Davis uses two different capos. In the clubs it appears to be a Hamilton capo which was around in the 1960s (although possibly not as early as 1961) but in other scenes he is clearly using a Shubb capo which was not available until 1980.
In the bathroom scene where John Goodman's character overdoses, a handicapped-accessible urinal is clearly visible on the wall. The movie is set in 1961 but public restrooms did not have handicapped facilities until the ADA was enacted in 1992.
Pappi calls Davis after he finishes the session, this scene is there in the beginning and at the end. Both are two separate shot twice(same scene recorded twice), where they are same as per the story line.If you see, pappi calls davis by right hand in the front and the back side shots in the beginning scene, but in the last scene, he calls him by his right hand from the front side shot and by left in the back side shot. With that davis's leaning and the woman crossing differs in both scene. When it is the same scene, why did they record that twice?
When Jean and Llewyn are arguing in the coffee shop (?) after she brings down his stuff, her hair changes repeatedly between shots. Her bangs change from pushed the side, to parted, to straight down and back in a very obvious way. She is never shown touching her hair.
When Llewyn gets dropped off in what is supposed to be Chicago, and again when he hitches a ride back to New York, it was obviously shot in New York judging from the distinctive electrified railroad tracks in the background, either Pennsylvania or New Haven Railroad. Probably the approach to Hell Gate Bridge.
Early in the film, Llewyn takes the subway downtown to Greenwich Village, and when he arrives at Sheridan Square, we see him coming up from the uptown platform, as if he had been traveling from the other direction. (He should have come up from the staircase across the street visible in the same shot.)
When the driver is arrested, the camera zooms to the ignition switch of the 1961 Buick. the keys are gone, but on that model the car would still start and run by turning the switch without a key. in the run position the key can be removed. in the lock position-full left-it cannot be restarted.
After Llewyn returns from his Chicago trip and is staying at his sister's house, the Etch-A-Sketch by the bed reads "Welcome Uncle Llewyn," written in capital block letters (except for the "U" which connects to the "N"). However, it is not possible to create unconnected patterns on an Etch A Sketch screen, as the stylus only moves in a connected line, so only cursive(script) style of writing is possible.