In the chapter ALL GOLD CANYON, which takes place in or before the year 1873, the prospector is singing the song MOTHER MACHREE, which was composed by Ernest Ball, written by Chauncey Olcott, and published in 1910.
In the Curly Joe scene Buster sings "His days of stud and hold'em they are done . . ." But according to Wikipedia, "Although little is known about the invention of Texas hold 'em, the Texas Legislature officially recognizes Robstown, Texas, as the game's birthplace, dating it to the early 1900s."
Immediately after Curly Joe (Clancy Brown) "commits suicide" by the hand (well, foot) of Buster Scruggs (Tim Blake Nelson) in the saloon at Frenchman's Gulch, a long shot from above reveals that all of the table's planks have chips or cards laid out on them in an orderly and undisturbed fashion, which would not be possible after what had just occurred.
In "The Girl Who Got Rattled" the wagons that were depicted where Conestoga Wagons. However, while they had been used as freight wagons in the East and South, they were seldom used on the trails to the West. They would have been too heavy for the trails. What was likely used is a Schooner, which would have been half the size of a Conestoga.
In the The Gal That Got Rattled, Billy Knapp tells Alice about the 1872 donation land claim granting married couples arriving in the Oregon Territory 640 acres of undeveloped land (320 for single male citizens). This was actually the Donation Land Claim Act of 1850, which ended in 1855.
After the Cowboy in Near Algodones is about to get hanged, for the first time, the horse wanders from its initial spot under the tree. If the rope around the Cowboys neck is long enough to let the horse wander that far, he would have landed on his feet if the lawmen had had luck fulfilling the deed.
Also, the rope changes angle in closeups vs in landscape footage.
In All Gold Canyon, during the shooting of the prospector and subsequent struggle, six shots are fired. The assailants revolver is a Colt Patterson model, an early percussion weapon with only a five shot capacity.
The goof item below may give away important plot points.
In the segment "The Gal Who Got Rattled", Gilbert Longabaugh's death is attributed to cholera. However, this does not fit his violent coughing before death. Cholera is an intestinal infection that results in severe diarrhea instead.