During the rifle marksmanship display at Maximillians ball, they use Pittsburghs rifle, a winchester 1894 which did not exist in 1866. Also the Americans carry colt SAA pistols not available until 1873.
Joe's saddle gun, a "new, Winchester repeating rifle", is an 1872 model; since the film is set "just after the American Civil War", to be correct, the gun should be a Henry "Yellowboy", circa 1864. (The earlier weapon had no wooden forearm stock and a brass receiver; the rifle Joe carries has a steel receiver and the wooden stock.)
Yellow Boy is the nickname of the 1866 Winchester, called such because of its brass frame. The Henry of 1860 was superceded by the 1866 Winchester because of its several significant improvements. There was no 1872 model.
When the caravan stops overnight and Cooper guards the stagecoach with the gold in it, as Lancaster approaches the stagecoach we can see Cooper looking inside and then he closes the door and starts to turn toward Lancaster. However, the scene immediately cuts to Cooper still looking inside the stagecoach and turns around in surprise to find Lancaster right behind him.
The very first scene was clearly shot in the town of Tepoztlan (State of Morelos), as apparently was a significant portion of the movie. Why the group would then choose to go north through Teotihuacan (past the Pyramids) in order to reach Veracruz (which is located on the East Cost) is beyond me, as it wouldn't make any sense at all. That's the equivalent of going from Des Moines to Minneapolis in order to reach Chicago.
The Gatling Gun used by Emperor Maximilian's troop with a drum magazine wasn't available until October 1884. In fact, since the Gatling Gun wasn't invented until well into the American Civil War 1860s it's questionable that Maximilian would have one in the base case.
The name of the Mexican city was originally two words, but now it is officially one word: Veracruz. However, at the time of the movie (in the late 1860s) both Vera Cruz and Veracruz were in common use.
When the wagon train is ambushed by the Juarezistas in a town, they make a break for it, fanning out and riding over an expansive field. The wagon tracks from previous takes are all visible in the grass.