While Christy is reminiscing about the Overland Stage with Hayes, he reminds him that they worked together on the line for twenty years. Before that, he says, he worked for the Pony Express. As the year is 1864, that would push his Pony Express experience to 1844 or earlier if you subtract Hayes' Civil War service. The actual Pony Express only was in operation for one year, from 1860 to 1861.
This takes place during the Civil War. And typical of movies about the period, everyone has a cartridge belt and pistol instead of the 'cap and ball' available at the time.
Characters use the word 'gunslinger' in conversation. Though it has been retroactively applied to the Old West, the word was actually only coined well into the 20th century.
The female characters in the film clearly have their hair set with hairspray. This product was invented during WWII and was made commonly available after the war.
As with the pistol anachronism, Miller had a Winchester model 1866 (or later) lever action rifle, despite the film being set in 1864.
The majority of the male characters wear pants with belt loops. These types of pants were not widely manufactured until the 1920s making them out of place in a film set during the Civil War.
The movie depicts Julesburg to be surrounded by tall mountains. The town is almost on the Nebraska border and is surrounded by flat land with distant hills only about 100 feet higher than the land in Julesburg.