Other mistake: The case of money is in the complete opposite physical orientation when Moss retrieves it from the air duct in room 38. When Llewelyn Moss hides the money in the air duct from room 138, he pushes it to the end of the ductwork with the closet rod and then pushes it to the left with the top of the case and handle going in first and the bottom slightly sticking out. So the top of the case (with the handle) appears to be pointing left in looking at it from 138. When he pulls off the grill in room 38 the next day we can see the top and handle protruding on the right side of the air duct (handle facing left, as he peers into the ductwork). Since we know from the motel room map, that room 38 is directly behind 138, with common rear wall, the top of the case and handle should be facing the right, (from a visual perspective), as you look into the ductwork from room 38 - and it is not.
Other mistake: When Llewellyn picks a cab to take in Del Rio, behind the cab that he takes is a cab with a rear license plate that reads J8R-725. Later in the story, at the crime scene, Llewellyn's wife drives up to the motel in El Paso in a cab with the same license plate number as the one in Del Rio. It's also the same plate number on the vehicle Llewellyn's wife pulls up to the house in after her mother's funeral. (00:37:00 - 01:36:50)
Other mistake: When Chigurh first visits Moss' trailer on the Monday morning after finding his truck, the mail, including phone bill, is already inside the door. Chigurh uses the bill to call Carla Jean's mom, and when stymied, reviews the bill for additional clues as to Llewelyn's whereabouts. He sees a call made on June 2 to Del Rio and uses that to determine his next search location. Problem is, the Monday on which he found the bill is June 2, 1980. As well, the mail is on the floor behind the front door when Chigurh picks it up, however there is no mail slot in the front door.
Other mistake: After Chigurh kills the deputy at the beginning of the film, the next shot is an overhead, downward view of the sink and the killer's arms only, as he washes the blood from his cut wrists. Your attention is naturally focused on the handcuffs and bloody hands in this brief shot, but watch the extreme right edge of the screen. Chigurh has very dark, almost black hair, however, a small portion of the actor's head is seen twice during the shot, revealing light brown, or blond-like hair. The actor appears to be purposefully leaning away from the scene in the very beginning, but inadvertently leans forward during the washing action and the camera caught the hair. I believe the director used a hand model for this one shot.
Other mistake: Chigurh's shotgun is a Remington 11-87 semiautomatic shotgun, yet in none of the scenes where he fires it do we see it ejecting an empty shell casing.
Other mistake: It would have taken two hundred $10,000 wrapped stacks of $100 bills to equal $2 million. There is no possible way that suitcase could hold two hundred of them.
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.