Corrected entry: In the episode where Luanne's mother, Lee Ann, comes back, Hank says that Luanne's father (Peggy's brother) is hiding out on an oil rig in the Gulf Coast. However, in a Thanksgiving episode (the one where everyone is stuck at the airport), it's mentioned that Luanne's father is in Montana.
Corrected entry: In the episode with Santa Ana's wooden leg. After Dale has made Cotton the fake driver's license, he holds it up and you can already see part of the word "Cheerios", showing that Dale used a cereal box to make it. Cotton would obviously notice when he took the license.
Corrected entry: In the episode where the family visits Peggy's family's ranch in Montana, Peggy's mother is mad because Peggy didn't stay on the ranch and marry the neighbors' son. However, in an earlier Valentine's Day episode, where Peggy learned that Hank had mono, we saw Peggy and Hank as a couple in high school, with Peggy going to West Arlen High. This means that she was not living in Montana as a young adult (or at an age when her mother thought she would be old enough to marry).