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.]
Continuity mistake: When Boss and Charlie are crossing the flooded main street (before rescuing the dog), Boss is holding his shotgun pointing up into the rain in one shot, then in the next shot (from a different angle), it's pointing down, then up again and so on.
Continuity mistake: Near the beginning of the movie, after the rainstorm, Charlie and Mose are digging and flopping around in the mud to get the wagon out of the hole. They are both covered in mud. As soon as they get the wagon out of the hole, Button says "Here comes Boss". As Boss rides up, Charlie is removing his gloves, which are now dry and free of mud.
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.
Continuity mistake: Charlie's dog, Tig, is referred to once as a "she" and once as a "he". In the scene where Charlie and Boss are heading back to town to find Mose, Button indicates the dog wants to go too. Charlie refuses, saying "She's got the heart ... she ain't got the legs." Later, in the scene where Charlie buries Tig next to Mose, he says, referring to Tig, "... he was more his dog than mine."
Other mistake: During the shootout scene, Kevin Costner is firing a single revolver while advancing across a street. He fires at least 10 shots from a six shot revolver without reloading. In just the part of the sequence where he fires multiple shots in rapid sequence into a single guy he fires 7 shots.