Travolta's character sees that Paul has a McClellan saddle and trapdoor Springfield rifle. He 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 is visible hiding behind the bushes between the horse and the priest at 1:07. At first i thought he's part of the scene and waited for them to have a duel with Ethan Hawk but nothing until the Main titles shows up.
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.