Other mistake: Early in the film Wayne and others have two steers tied, lying on their sides for branding when they are approached by Mexicans. Following a dispute Wayne kills one of them,a grave is dug and a brief service is held. Following this (which must have taken at least a half-hour) the same cows are still tied up; it is doubtful that a competent cowboy would have allowed them to be tied in that position for that long.
Factual error: The film begins in 1851 with Wayne leaving a wagon train & heading south. During this trip he meets young Matthew Garr who he then raises. 14 or 15 years pass, making it 1865 or 66, and Wayne has established his ranch. He and all of the characters are armed with Colt Peacemakers, which were not introduced until 1873.