Factual error: Though extremely modest on today's standards, the dress worn by Clara to the hoedown shows far too much cleavage for the time. No schoolteacher would ever wear a dress like that in the 1880s.
Continuity mistake: In the scene when Billy is shooting Doc's handcuffs, Billy's revolver changes several times, shot by shot. Watch for the front sight to appear and disappear between the POV Doc shot and the medium distance shot, and for the entire finish of the gun to change at least twice.
Continuity mistake: In one of the final scenes where Tom Selleck has a gunfight with Alan Rickman, the time of day during the few minutes (in movie time) the scene takes place varies from noon (full sunlight) to dusk. Just prior to the gunfight, when Selleck is getting ready to draw on Rickman and his two henchmen, there are almost no shadows and there is bright sunlight indicating it is in the middle of the day. Just after the gunfight there are now long shadows on the characters and moments later the camera pans across the hills and the sun is setting.
Suggested correction: Shadows exist before and after try to watch it again.
Revealing mistake: In the extended version of the film during the buffalo hunt, there is a shot of a buffalo making a turn and in the distant horizon, you can briefly see a modern radio tower on top of a hill.