Other mistake: At the end of the episode we see Hank at the motor vehicle office alone which means he drove himself there. Dale later comes in and helps to get Hank's license changed back to male. Afterwards Hank gets into Dale's van and puts on his seat belt implying Dale is driving him home. Hank should have gotten into his own truck.
Character mistake: When Peggy is meeting Lucky's sister at Luanne's baby shower, she mentions that she lives across the street. However, the baby shower is taking place at Peggy's house, as evidenced by the layout of the house and the wallpaper.