Factual error: The movie is set in 1882, however there is a scene where he meets Doc Brown with his DeLorean. Back to the Future Part III took place in 1885.
Continuity mistake: When Clinch and his gang start to chase Albert, from his house, many of the sheep start running and moving out of the way, even kicking up dust. When the camera angle changes, none of the sheep are moving and there's no kicked up dust.
Deliberate mistake: While done for comedic effect, the ram's penis as we see it is not what a real one looks like, most noticeably is the missing urethral process.
Continuity mistake: In the beginning when Stark is talking with Charlie, when the camera is facing Stark, the buildings' shadows go from the viewer's right to left. After he falls down from being shot at, the shadows are now going in the opposite direction (the camera angle changes to face Charlie, but the shadows still go right to left).
Continuity mistake: When Anna is first teaching Albert to shoot, and he says he's going to shoot a full load, he cocks the hammer back. In the next shot, the gun isn't cocked, and he cocks the hammer back again.
Continuity mistake: As Albert and Anna walk off at the end of the final gun fight, watch their arms. From the front they're only holding hands. They call the dog to them, and instantly the shot from behind shows them with their arms thoroughly wrapped around each other.
Continuity mistake: Anna hands the unspiked drink to Foy. Top glass was spiked, placed on Anna's right. She hands him one to her left.
Continuity mistake: Foy craps in two hats, then sets them down ~1ft apart. When he stumbles forward (foot placement implies he kicked the 2nd hat over) - the field of view/angle shows only one hat visible. The other hat should be in frame.
Factual error: When Albert escapes Clinch's gang on the train, a marking on the boxcar indicates that its roof was replaced on 10-24. 1824 was long before this type of rail car was built, and 1924 would be 42 years after the movie is set.