Factual error: In the final gunfight, we see a close-up of Charley fanning the hammer and rapid-firing his six shot Colt Single Action Army nine times in a row. [Kostner has stated in interviews that this occurs because a short scene of him switching revolvers (he had a second revolver in his belt) was left on the cutting room floor. Still a mistake, but there's the reason.]
Factual error: When the open rangers are camping, at the beginning of the movie, you can see what appears to be ski runs coming down a distant mountain. There were no ski resorts of this type in the 1800s.
Factual error: Kevin Costner fires 18 shots from one six shooter revolver, (and those 18 are just those which can actually be seen fired on-screen), during the big shoot-out at the end of the movie. A few more are heard and are implied to be from him - but not shown on screen, because the camera is jumping back and forth to different shooters. And even though he says, (in interviews), that there was a second revolver in his belt, which wasn't shown, that he switched to, he still would have needed a third revolver, even if those implied shots didn't come from him. They show him (during the fanning shot), firing one six gun far more than six times, without taking the camera off him.