The Breakup - S1-E16
Continuity mistake: When Jeff Derrington arrives on horseback at his ranch, his wife and a baby carriage are in the yard. The carriage is covered by a white blanket. A close-up shows a baby boy in the carriage, even though Jeff never removed the blanket.
Continuity mistake: While Gene plays guitar and sings "Back In The Saddle Again," a close-up shows the chuck wagon cook waving his ladle back and forth in time with the music. In the following long shot, the cook is leaning over and dipping the ladle into a stew pot.
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.