Factual error: The narrator mentions that the Cheyenne tribe split in half in northern Nebraska. The scenery would suggest otherwise, as there are no mountains that high in Nebraska.
Factual error: When the "U.S." soldiers open fire on the Mexican cavalry, they employ a machine gun. The only two rapid-firing weapons in that time period were the Gatling gun, which used a magazine or drum of rounds and was fired by turning a crank, or the "Mitrailleuse" volley gun, which required at least two men to operate it, one to load the ammunition blocks, and the other to turn, once again, a crank to fire the weapon. The gun pictured has a single operator and neither a crank, nor any visible cartridge feed.
Factual error: In a scene set in 1871, several newspaper articles get printed on Moe's face as he falls onto a printing press. Curly Joe reads that "AT&T is splitting two for one." American Telephone and Telegraph Company was founded in 1885.