Factual error: Bill Kempt rigs the sapphire asteroid with rocket motors to divert it toward the Moon. The motors are old and cranky, and to ensure that they fire on time he must, at some risk, lash himself to the rock and manually start the ignition. Upon lighting the engines he has several seconds to cut himself free, but in the scene he's shown swinging weightlessly as he snips the cable. If the asteroid is accelerating, he ought not to be weightless, but rather should be hanging behind the rock on his tether.
Factual error: When the Confederates enter the plaza to be greeted by the Mexican authorities, the Stars and Bars are raised below the Mexican Flag. However, during Maximilian's reign, the Mexican Flag was completely different from the flag shown.
Factual error: Campbell is armed with what is described by Wayne as a "buffalo gun", a large bore rifle known for its power and substantial recoil. Campbell shoots a wild turkey with the gun and causes the meat to be severely damaged. Wayne comments, "Too much gun" emphasizing the power of the gun. However, when Campbell shoots the turkey with this "buffalo gun" there is no visible recoil.
Factual error: Near the end of the film Butch is complaining about the living conditions they have to endure - jungles, swamps, snakes, night work - and Sundance sarcastically retorts "Bitch, bitch, bitch!" In 1908 the term meant just what it literally means: "Female dog." It did not adopt its current meaning of "complain" until much later. At the time the film is set - outside the context of "female dog" - it was considered to be a serious obscenity, and it would not have been used to describe something as ordinary as someone moaning about his living conditions.