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.
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.
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.
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.
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.
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.
Grass on the Streets and Weeds on the Rooftops - S4-E10
Plot hole: Beth surprises Jamie in the act of disposing of his father's body at the train station. But Beth doesn't learn about the train station until season 5, episode 8. So, how did she know where to catch Jamie in the act?
Character mistake: The Native American brother points to the Bronze Star and refers to it as the Silver Star.
Continuity mistake: In the previous episode Dutton fired all the woman cowboys and kicked all women from the bunkhouse. Early in this episode Teeter is visible working as they round up cattle on the ranch. Yet a few minutes later she comes to John and Rip begging for her job back.
Suggested correction: In the scene you're referring to, the girl you see is not Teeter. It's a girl with Travis' crew.
