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).
Factual error: 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.
Factual error: As Sheriff Ed Tom Bell is driving up to The Desert Sands Motel, which is supposed to be located in El Paso, Texas, there is a sign on the right hand side which says "Route 66" - advertising a business on site. Route 66 did not go through El Paso - it was a few hundred miles to the north.
Factual error: The international bridge was in 1980 staffed by US Customs agents who wore blue uniforms. The agent questioning Brolin's character is wearing Border Patrol green.
Factual error: When he first gets to Del Rio, Brolin's character buys a pair of Larry Mahan boots to replace the ones he lost at the river. He later hitch-hikes to Eagle Pass, gets wounded, and crosses to a hospital in Piedras Negras. He comes back into the Del Rio store for 'everything else', but he should still be in Eagle Pass, not Del Rio.
Factual error: The phone bill shows several calls from Area Code 210 (San Antonio). This Area Code did not exist until 1992, some 12 years after the movie is set.