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.
King of the Hill (1997)
1 deliberate mistake in season 9 - chronological order
Starring: Brittany Murphy, Pamela Adlon, Mike Judge, Kathy Najimy, Johnny Hardwick
It's Not Easy Being Green - S5-E16
Factual error: Boomhauer's car, Ms. Sally, has a Texas flag license plate on it. These plates were not issued until 1992, but Ms. Sally was driven into the quarry in the late 70's or early 80's.
Hank: Calm down, Boomhauer! I can't understand a word you're saying.
More trivia for King of the Hill
To Sirloin with Love - S13-E20
Question: What is Boomhower's occupation?
Answer: Jeffrey Boomhauer is a Texas Ranger as can be seen in the final episode at the end when he sets his wallet down, it flips open revealing a Texas Ranger badge.