The Sheriff of Santa Rosa - S1-E23
Other mistake: Gene is chasing Ted Nolan, who is believed to have ties to a gang of cattle rustlers. Both men are on horseback. A long shot of Gene riding across a range is followed by a long shot of Ted riding across the same range so it appears Ted is chasing Gene instead of the other way around.
Other mistake: Lucy Lawrence enters the stage depot in Bentonville and introduces herself as the new schoolteacher. A young boy exclaims, "School! Phooey!" Mrs. Lawrence says, "Well, school isn't all reading and writing and sums, Edgar." She had no way of knowing his name.