1. Hank Hill is a literal sperg but is on the higher-functioning end so he was able to make it out on his own in the real world. Between undiagnosed autism and Cotton as a father, this is part of why Hank's so eccentric and has the hangups he's known for.
2. Peggy suffered brain damage when she fell from the plane. It wasn't enough to impair her in any cognitive or intellectual way, but it was enough to fundamentally change her personality and make her the egotistical pseudo-intellectual in the later seasons. In the first three seasons, she was a lot more grounded with only a few "Peggy" moments.
3. Dale Gribble knows about John Redcorn and has the entire time, but intentionally feigns total ignorance since he loves Joseph and Nancy too much to rock the boat. He's also well aware that while John Redcorn is Joseph's father, he's Joseph's real dad.
4. Bill suffers from a lot of PTSD related to both his abusive childhood and the abusive marriage to Lenore. This is part of why he crashed and burned as badly as he did. He may have some sort of underlying condition that exacerbated it.
5. Boomhauer is a Texas Ranger and his mentions of being on Workman's Comp in the early seasons was a cover story. More specifically, Dale is one of his confidential informants because he trusts Boomhauer and wants to keep certain unsavory figures away from the Gun Club. This may have been part of why Mad Dog went to prison.
6. Relating to the above, Boomhauer was the one who actually called in the Texas Rangers when Debbie died but Peggy took the credit because she's a fan of Walker. Because he's a close friend of the potential suspects, he can't work on the case.