As the camera pans across the riders after they arrive at the ranch, you see the sheriff's horse with no rider. In the next scene they show the sheriff getting off his horse. The scenes were out of order.
At the start the viewer is informed that Tom Barkley was killed 6 years ago. Then at Tom Barkley's grave, the viewer sees on his tombstone that he died in 1870. Therefore, the setting (at least for the first program) is 1876. But Heath pulls out an article that he cut out of a newspaper that covered Tom Barkley's funeral (which would have been 1870) and which had a photograph of Tom Barkley. The problem is that newspapers in the 1870s did not have the technology to reproduce photographs. In fact the first photograph to be published in a newspaper (a "photomechanical reproduction of a photograph") was the Daily Graphic on March 4, 1880 (source: The Library of Congress).
Vincent Gardenia's character is credited as "John Sample." During the show, everyone calls him "Frank."