When Sheriff Cooper leaves his horse to go after Willie in the final sequence he is carrying his canvas ground cloth. He does not have it in any of the following shots.
In the pool room scene, the betting bar patron places the cue ball illegally outside "the kitchen" during his rack break. In addition, he is breaking from the wrong end of the table: one can clearly see the "foot spot"-- the black spot where the rack is placed-- is empty.
Many of the hats worn in the film are not the style worn during the early part of the 20th century. Some in fact, could only have been sewn using machines created in the 1950s, nearly half a century after the film's setting.
Willie Boy's original clothing and Cooper's haircut are more 1960s that 1900s.
Many of the shirts worn by the men throughout the film are in the style of modern shirts. They have buttons that run their full length in the front and can be put on by pulling them over and around the shoulders. These types of shirts were not manufactured until the 1920s, about a decade after the 1909 setting of the film.