Visible crew/equipment: A crew member seen standing on the far left of the frame when Llewelyn is being chased down the river. (00:19:34)
Factual error: When Chigurh is in the gas station and throws the wrapper on the counter, the "Nutrition Facts" are visible on the label. Set in 1980, the "Nutrition Facts" label wouldn't have been available for at least another fourteen years, as nutrition labels were started in 1994.
Factual error: When Chigurh is in the gas station talking to the clerk, behind him on the shelf is a pack of Jack Link's beef jerky. The movie is set in 1980, but Jack Link's did not start selling beef jerky until 1986.
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.
Suggested correction: He might have meant 12th Infantry Regiment. From Wikipedia: "Three 12th Infantry battalions deployed to South Vietnam with the 4th Division from August through October 1966."
If he said "battalion" but meant "regiment", then it's still a valid mistake for saying it wrong and being believed.
Regiments have not existed as functional units in the US Army since shortly after Korea; they are simply historic names associated with various battalions. Marine battalions are not numbered higher than 4 in any regiment, and in any case do not carry an explicit designation of "infantry."
Revealing mistake: In the scene at the motel where Chigurh kills three men, he goes to sit on the bed where he removes his socks. In the background one of the 'dead' men opens his eyes and looks around.
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.
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.
Factual error: At the motel where Brolin's character first hides the money in an air vent, and when the hitman arrives to look for him, a silver 1985-1990 era Dodge Aries is parked prominently in the parking lot, despite the film's events taking place in 1980. (00:45:20)
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.
Factual error: Despite the film's events taking place in 1980, several scenes feature a much newer 1986-1990 series Chevy Caprice (evidenced by the flush-mounted tail lights). The most obvious example is in the very first scene showing the rear of such a police car. (00:02:00)
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).
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)
Continuity mistake: When Harrelson visits Brolin in the hospital, the small white flowers to our right are in random conditions of wilting throughout the scene, starting quite down, then way up and everywhere in-between. (01:14:50)
Factual error: When Moss tells the border guard "I've got an overcoat on", a 1982+ Pontiac Grand Prix approaches behind him, though the film is set in June 1980. (01:27:50)
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.
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.
Factual error: When Josh Brolin is leaning against the guard wall outside the motel, there is a Carl's Jr. visible in the background. Carl's Jr. did not open stores in Texas until several years after the movie is set.
Visible crew/equipment: When Moss is talking with the security guard at the border bridge, you can see the camera and the cameraman next to Moss in the reflection of his sunglasses. (01:27:40)
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.
