Deliberate mistake: Why wouldn't Hank just use a credit card to cover the outstanding payment he owes on his insurace? It was established in the episode Rich Hank, Poor Hank that Hank has an emergency credit card and could easily use that and would be covered immediately. His panic over not having insurance would outweigh any problems he might have with using his credit card and the fact that he is dealing with an insurance company there is no conceivable way they wouldn't accept a credit card or ask if he has a credit card to cover the payment. The mistake seems to be deliberate as it sets the story up for Hank going somewhat over the edge with protecting the house.
Continuity mistake: In the scene when Lane Pratley comes into the woman's changing room after the first game he is holding the player's cheques by his waist. When the shot changes to a closeup of him the cheques have instantly moved to Lane holding them next to his chest.
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.
Continuity mistake: At the beginning of the episode, after Peggy's mother calls, Hank says "What's it been? Twenty years?" But they spoke with Peggy's mother during the events of the episode "Happy Hanks Giving." Hank spoke to her on the phone, Peggy shouted at the phone, and Hank commented on Mrs. Platter not approving of propane.