Continuity mistake: The lady at the bar has a double shot of whisky. Walker asks for some water. As the scene plays, it goes back and forth, showing their faces and drinks on the bar. They are talking and not drinking, but the lady's drink empties down to the ice cubes. (00:03:29)

Factual error: Jamie is looking at his birth father's Montana State Prison inmate identification sheet. On the sheet, it lists his Social Security Number (SSN) as 4142-77-89332. However, in the United States, an SSN is a nine-digit number. (00:25:07)

Factual error: The Governor arrives at the ranch in her official vehicle. However, the vehicle has US Government license plates. A State Governor is not a US Government representative, so the vehicle would have State plates. (00:16:41)

Continuity mistake: Beth arrives at Rip's house and drinks a beer, with the big logo on the can facing the camera. An instant cut later, the can has turned around.

An Acceptable Surrender - S3-E3
Continuity mistake: When the governor arrives at the rodeo and sits next to John, he holds a beer with his right hand. A shot later, it's in his left hand.
The Beating - S3-E7
Continuity mistake: Near the end of the episode, Kayce has tracked his stolen cattle to a trailer. He bangs on the door, identifying himself as a livestock agent. The lock clicks audibly, so Kayce runs around back where a gunfight ensues, and he kills the cattle thief. Moments later, he is back on the other side of the house where he was knocking and hears a child's scream. Rather than running back around to the side of the house where the dead guy is, he enters the now unlocked door to find a little girl crying over the dead guy.
Continuity mistake: When the bikers are grilling on the ranch, there are only 10 bikers. Butin the various shots that show the bikes, there are 12 bikes (2 groups of 6).
Continuity mistake: Beth drinks beer and cleans her mouth with her arm, while Rip raises his right arm and takes a sip. An instant later, his arm is lowered and extended to embrace Beth.