Revealing mistake: In the scene out West with the buffalo, notice the car driving in the distant background.
Continuity mistake: There is no way the cow (a Hereford I think) could have given birth to that calf (a Jersey or something like that). [The mom is a mixed-breed BEEF cow, the calf a purebred Jersey DAIRY calf. An amazing feat of animal husbandry.]
Other mistake: Bandoleer rounds don't fit any weapon in the show. When Pierce tries the Gatling gun, there is no magazine in it.
Continuity mistake: When James goes to help up Michael after Jake punches him, they walk off to the horses without picking up Michael's rifle that was next to him on the ground. He somehow has it to use later on in killing the man in the bell tower. (00:50:50)
Factual error: When the riders are watching the wagon train, in the background you can see a communication tower with conical speakers.
Continuity mistake: In the first shot of the dead man hanging form the tree, his head appears to be about 12" from the tree limb. After Mattie climbs up to cut him down, his head is several feet from the tree limb.
Other mistake: There's a horse that has apparently ridden up a cliff, and an electrical burning brand that can be changed onto different flame settings.
Continuity mistake: When Sharon Stone confronts Gene Hackman at the end, she throws the marshal star at his feet. It is an inch or two in front of his boots. After he is shot, he gets flung backwards several feet. Stone then picks the star up and throws it to Russell Crowe. She picks it up from behind Hackman's body, several feet away from where it landed but still sticking out of the sand the same way.