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)
Continuity mistake: When Moss unloads the shotgun onto the diving Chigurh, Chigurh's right thigh is towards Moss, but later when C fixes his wound, it is his left thigh he's repairing. (01:04:14)
Factual error: When Josh Brolin is leaning on the cinder block fence at the motel towards the end of the film, behind him are some mountains and a tall building. The scene is set in El Paso, Texas but the mountains shown are the Sandia Mountains which are east of Albuquerque, New Mexico.
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.
Factual error: When Anton Sigurh stopped to refuel at the gas station in the middle of nowhere and the owner told him, "I seen you was from Dallas," that's a factual error. In Texas, the DMV issues license plate numbers at random, so that the man couldn't "read" Sigurh's tags to determine where the vehicle had been registered. Therefore, the very tense scene that follows, where the poor man is one coin toss away from getting killed, is based on a factual error.
Factual error: Carla Jean says she works at the Walmart in Sanderson, Texas. There is no Walmart there, nor has there ever been. The nearest one is 65 miles away in Fort Stockton.
Continuity mistake: In the scene where the two sheriffs inspect the burning car, Wendell puts his thumbs in his back pockets, where they remain for the next two shots from behind. Shots from the front, however, have Wendell's left hand in front, with his thumb through his belt. (00:27:30 - 00:28:30)
Continuity mistake: During the gas station scene, Chigurh is continually eating from his bag of nuts. During the conversation between Chigurh and the attendant, as the camera cuts back and forth between them, Chigurh keeps eating a nut from behind, and then from the front, his hands are by his side and he eats a nut again. This occurs several times throughout the scene.
Answer: It was a different gun. He kills Carson with a shotgun, while the gun Moss picks up is a silenced SMG by the looks of it.