Continuity mistake: Chigurh is cut deeply on his wrists when choking the officer with his handcuffs at the beginning of the movie, but later when he is doctoring the wounds on his leg, his wrists are completely visible and there are no recent injuries.
Continuity mistake: When Chigurh places his handcuffs around the police officer's neck to choke him, the handcuffs are more like manacles and contain 7 or 8 links between the cuffs. When he goes to wash the blood off of his wrists and drops the handcuffs in the sink, they are much smaller, containing only 3 links between the cuffs. (00:03:05 - 00:03:45)
Factual error: The glass milk jar in the Moss trailer that various characters drink from is labeled Promised Land Dairy. Although the movie is set in and around 1980, Promised Land Dairy didn't start producing milk products until around 1990 (http://www.promisedlanddairy.com/web-content/Our%20History.html).
Continuity mistake: When Llewelyn is talking to the woman beside the pool at the Sands Motel, his gun satchel is by his side. During the cutaway shots back and forth between Llewelyn and the woman, the distance between the gun satchel and Moss changes several times.
Character mistake: When Moss is arguing with the border guard at the Eagle Pass international bridge, he claims that he is a veteran of the "12th Infantry Battalion." There has never been such a thing as the 12th Infantry Battalion in either the Army or the Marines. Rather, they are based on a structure of 3-4 battalions per numbered regiment (i.e., 1st Battalion, 3rd Infantry Regiment/2nd Battalion, 5th Marine Regiment, etc). The film takes this seriously, as the guard, a veteran himself, buys Moss' story.
Factual error: In the desert "drug deal gone bad" scene, the red Ford Bronco has a blue oval in the grill. Ford did not start using blue ovals in the F-series until 1981. The movie was set in early 1980, per Agnes' tombstone, and 1981-model production didn't begin until August 1980. Further, the truck shown is modified, battered and rusty - certainly aged and well-used.
Continuity mistake: In the gas station scene, Chigurh places a crumpled candy wrapper on the counter as he is intimidating the owner, and the camera stays on the wrapper for a few seconds as it unwrinkles itself. Moments later, as Chigurh reveals the coin toss result, it is a completely different, blue and white wrapper.
Revealing 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: 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 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.