When James leaves the train to ride to the town he is wearing a rough work shirt and bandana under a bolero jacket When he rides in to town he is now wearing a white dress shirt a vest and an ascot under his bolero jacket.
After West pulls the card out of the drawer, he makes no motion to shut it, but it is closed in the next shot.
Between 8:05 and 8:40 pool ball changes position on table.
After Jim West runs into his old flame Lydia Monteran (Suzanne Pleshette), she gets angry with him and shoots at him with her pistol. Even though it is plainly shown as having the standard six chambers in the cylinder (and thus holds only six bullets) she fires the pistol seven times in chasing James out of the room.
At several points you can see metal hurricane lanterns. Many shown are Dietz monarch lanterns with the art-deco style that was not introduced until late 1937 and would not have existed yet in 1870-1890. These metal type lanterns were much more rare than the glass fount type Victorian table lamp, and typically had square tubes. Something like a Dietz #0 lantern circa 1888 for example.
When Colonel Shear is briefing West, he indicates a map of New Mexico and refers to it as "The Southwest Teritory". Although the borders changed a number of times, the only part of the current US that was ever called the Southwest Territory (officially "Territory South of the River Ohio") is the current state of Tennessee.
Lydia's cockatoo clearly chirps "What's your pleasure?" appropriate for a bordello. But the closed caption states "Watch the feathers".