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.
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.
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.
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?