A sign is visible during one of the Carson City scenes during the latter part of the picture showing the words 'Bulldog Drummond's'. He was a fictional British detective that first appeared in a 1920 novel, almost forty years after the movie's setting in 1881.
When Chon Wang is protecting the Indian kid, two warriors on horseback arrive. In the first shot, one of them has distinct black and white war paint on his face. In the next shot he is replaced by a different rider, but then returns later in another scene.
When Wang says, "The sun rises in the east, blah, blah, blah," O'Bannon's left arm changes from pointing at Wang to being in the tub in the next shot, and then in the next shot his arms and shoulders are further out again.
If Chon Wang is an Imperial Guard, then that means that PeiPei is an imperial princess (i.e. Emperor's daughter). In the movie, the guards all call her "Gong Zhu", but that refers to a king's daughter. An imperial princess is supposed to be called a "Ge Ge."
When O'Bannon is buried in the desert up to his neck, Chon Wang gives him a pair of chopsticks to dig his way out. The chopsticks clearly have tapered ends, which is characteristic of Japanese chopsticks. Chon Wang would have given O'Bannon Chinese chopsticks, which have blunt ends.
During the gallows scene, when the Indian Wife is loading the rifle, she is placing the cartridge into the top of the tubular magazine with the bullet pointing down. The rifle is an 1860 Henry so the magazine must be loaded from the top with the bullet end up, or it will not chamber into the breech of the rifle.
By the end of the train robbery most of the train cars have been uncoupled from the train, and most of the cargo lost (the load of logs, the safe). Throughout the scene, the locomotive keeps chugging along as if nothing has happened. The locomotive crew would have noticed their load getting lighter unless they were dead or unconscious, and there is no implication that this is the case.
When Wang and Roy are talking in the jail cell, Roy mentions "...your friends on the train?" to Chon, as if he knows about the other guards. However, Roy couldn't have known, because he never visited the caboose during the robbery.
When the horse carriage knocks over the hanging gallows, Roy falls to the wagon below. Before he falls, his hands are tied behind his back; as he falls, you can see a piece of rope tied around each hand, which are separated (when he places his hands together, this gives the appearance that his hands are tied together).