Continuity mistake: Peggy Hill's mother seems to change over the course of the show. Prior to the ninth season, whenever Peggy's mother is seen (in the present or in flashbacks), she is portrayed as an older version of Peggy. In the ninth season's premiere episode, Peggy's mother is a lean, leather-skinned rancher who disdains Peggy and lives on a secluded ranch. The change in facial features and appearance is too much to just be a change in style as well.
Continuity mistake: In several episodes, the color of Alamo Beer that Hank, Dale, Boomhauer, and Bill drink, changes color. In "Uh-Oh Canada" the beer is yellow, but in "Death of a Propane Salesman" when Hank pours the beer into a glass, it is brown.
Continuity mistake: Throughout the first couple of seasons, Hank's first truck switches between automatic and manual transmissions. This is most obvious in the episodes "Chasing Bobby", in which it has a manual transmission and "Texas City Twister", in which it has an automatic transmission.
Continuity mistake: The ages of Hank, Peggy, and Didi (Hank's stepmother) are inconsistent throughout the show. In the season one episode "Shins of the Father", Hank states that Didi went to kindergarten with him, so they are the same age. In the season four episode "Peggy Hill: The Decline and Fall", Hank mentions that Didi is three years older than Peggy. Therefore Hank is also three years older than Peggy, if he and Didi were in the same kindergarten class. Finally, in the season five episode "Luanne Virgin 2.0", Hank says that he and Peggy were already married when they were eighteen. This is not possible if he and Didi are the same age and went to kindergarten together. He would have had to marry a fifteen-year-old Peggy if he was married by age eighteen.
Continuity mistake: In earlier episodes, Luanne is very knowledgeable about cars. This is shown in "Shins of the Father" (Season 1). In "Jumpin' Crack Bass" (Season 2), she does repairs on Hank's truck - and Hank is known to be protective of his truck. As the series goes on, she becomes a stereotypical "dumb" promiscuous type, with no apparent expertise in cars.
Answer: If you are talking about the "Thou shalt not do this, thou shalt not do that" song, I'm not sure if a song like that actually exists. Green Day, the guest voices on the episode, might have just been improvising to keep their appearance from being too obvious.