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.
The Apocalypse of Change - S5-E10
Other mistake: S5 E/0: The Apocalypse of Change - Tate is wearing a ball cap with a buffalo on the front, which would be fitting since his family's business is cattle ranching. Since the Dutton family are proud residents of the State of Montana, it's strange that Tate would be wearing a ball cap with the State flag of Wyoming. (00:15:08)
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.
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.