Just moments after Paul and Abby get out of the bath, Abby's hair is completely dry and fluffy as if she's never been wet.
When Paul leaves the town, he is shown to travel far and into the evening yet as he is mourning his dog, the camera pans from him to the town seen to be nearby.
Marshal Clyde Martin (John Travolta) questions whether Paul deserted the army when fighting Indians in Kansas or Oklahoma, since the Civil War was over. Oklahoma was called Indian Territory until 1890, and wouldn't have been referred to as Oklahoma until after the Indian wars were over.
A crew member is visible hiding behind the bushes between the horse and the priest at 1:07.
There are no mountains near Denton Texas, though Texas is not mentioned.