Factual error: The intro takes place in March. The trees in the background say otherwise. In the mountains in March, leaves are usually not fully developed on trees until April at the earliest. The scene was likely shot in the fall.

Cigarettes, Whiskey, a Meadow and You - S5-E6
Continuity mistake: When Mo arrives at the rally, he shows his badge to a soldier. He either holds it from the upper or the bottom part, depending on the shot.

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.
Continuity mistake: When Beth leaves home, Rip raises his hand, about to drink his coffee. An instant cut later, his arm is lowered, and he is repeating all movements.
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.

The Unravelling: Part 2 - S1-E9
Continuity mistake: When Beth and John are talking right at the end of the episode, her messed-up hair suddenly appears brushed between shots.
Other mistake: The excavator with the rotating bucket wheel that is shown in the opening is turning backwards from the direction required for it to actually dig.

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)
Continuity mistake: In last episode of S3 Jimmy decides to ride a bronco in the corral and right before he mounts he takes off and discards his wrist brace. In S4 episode one, he is found by barrel racer, and he has the brace on his wrist.
Phantom Pain - S4-E2
Continuity mistake: Toward the end of the episode Rip and young Carter come home for dinner. The boy sits down at the end of the table and Beth hands him his food. In the next shot and from then on a large glass of orange juice magically appears before him.

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: The main character is chasing after the guy in white. Right before he falls, the main character shoots him in the left shoulder. The mark disappears from his shirt after that.
Suggested correction: The guy was shot in his right shoulder not his left, when his head hit the rock, his left shoulder (not his right) is exposed.
Continuity mistake: At the end of the episode, when he does the carjacking, the car pulls away, and the car in front has the same licence plate as the car they are in.
Continuity mistake: Sarah goes to Jamie's home after a difficult day, and Jamie comes in shortly after he has been "rescued" by the new governor. After a terrible fight, Sarah goes over and grabs an empty glass from the top of the bar. The glass is suddenly filled with ice when she drinks the vodka.
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).
Phantom Pain - S4-E2
Continuity mistake: When the guy comes out on the tarmac at the airport, and turns around, watch the sun. It is a different time of day as the sun angle changes in seconds between shots.
Plot hole: SPOILER! Jamie Dutton is blamed for Beth being sterilized. But shouldn't the doctor be blamed for not informing the patient before the operation?
One Hundred Years Is Nothing - S5-E1
Continuity mistake: How is it that Carter has grown so much in 9 months? He looks 2 years older.