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.
Continuity mistake: Beth offers Rob a cigarette and places her cigarette case on the table, setting her gold lighter upright next to it. Although Rob doesn't immediately accept her offer, the lighter's position changes in subsequent shots—first standing upright, then lying flat on the table, and finally back to being upright again. (00:49:40)

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: 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.