Continuity mistake: When Button is picking his feet Robert Duvall tells him to move downwind. After he does so, you can see many cattle on the hill behind him. The scene cuts back to Duvall and Costner. Seconds later cuts back to Button and the cattle are gone.
Factual error: In the final shootout, a man is shot with a shotgun, and the blast comes through a wooden wall. It blows his body clean across an entire street outside the building, and he hits the wall of the building on the other side of that street. This never happens with firearms. No one is ever lifted off their feet, let alone blown across entire streets, etc. Physics declares that for this to happen, the shooter of the gun would have to be blown back with an equal and opposite force.
Answer: I believe he is the one being chased by the townfolks, after the gunfight is over.