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.
Revealing mistake: When Chigurh is preparing to blow up the car in front of the drugstore, he uses a piece of cloth as the fuse. He removes the gas cap, places a piece of cardboard over the opening, and lays the cloth on the cardboard. He then lights the cloth and walks into the drugstore. After the flames burn through the cardboard and reach the fumes from the gas tank, the car explodes. If you watch the burning cloth as he walks into the drugstore, you will notice that it never moves, not even when the car explodes. If the explosion had been real, the burning cloth would have been blown away from the car by the hot gases expanding out of the gas tank opening.