Factual error: At the very end of the movie, right before Javier Bardem is in the car accident, there is a shot out the driver's side window, past his face. In one of the driveways he is passing, a new Subaru Forester sits parked. The film is set in 1980.
Continuity mistake: During the dialogue between Moss and Wells at the hospital, there is an ashtray on the bedside table next to him changing position in various shots.
Continuity mistake: Near the end of the movie in the car accident scene, when Anton steps out of the car completely injured, the door's window appears broken in a way and then in a different one in a next scene.
Continuity mistake: After Chigurh kills the three Mexicans inside the motel room, the dead body of the second man with the meter in the hand changes position in two detached shots. At first he has his head on the ground, then he keeps it pressed from behind against the cistern toilet. (00:50:28 - 00:51:09)
Answer: "Blood Trail (end titles)" By Carter Burwell, the Coen's frequent composer. The Film does not have a soundtrack, but you can listen to it in Carter Burwell's website: http://www.carterburwell.com/projects/NCFOM.html.