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: 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.