The setting of the film is the beginning of the Pony Express, which ran from 1860 to 1861. Yet the Californian secessionists who try to stop the Pony Express's first-ever delivery use dynamite, which was not invented until 1867.
The founders of the Pony Express were not William Cody and James Butler Hickok but William H. Russell, William B. Waddell, and Alexander Majors. Hickok wasn't a rider for the Pony Express he only worked as a stockman
The 4 Indians are shown high up on a rock formation looking down on a valley when the rider goes through at full speed riding away from them. They are subsequently shown having overtaken the rider. This would not be possible due to the amount of time it would take them to come down off the rocks and get onto their horses.