Factual error: When York is explaining to Thursday about Cochise and the Indian agent's calumny, he states that Cochise took his people off the reservation, and crossed the Rio Grande into Mexico. The reservation in question would have been in the Arizona Territory, and the Rio Grande ceases to be the international border at El Paso, Texas. Cochise may have gone into Mexico, but he didn't cross the Rio Grande to get there.
Continuity mistake: Shortly after Lt. Col. Thursday is shot off his horse during the cavalry charge Captain York leave his troops on the ridge and rides to Thursday's aid. He helps Lt. Col. Thursday onto his horse and Thursday asks for and receives Captain York's sword. Minutes later Captain York is back with his men and is wearing another sword. Where did it come from?