Plot hole: It makes no sense why the producer has not got Hank to sign a release form or even talked about it. Throughout the episode Hank is upset by the fact that Dusty's reality show is featuring him. While Hank might not be aware of a release form, the producer would be fully aware if Hank did not sign one all the footage and most of the show would be unusable. Being that Hank was so against the project, this would also make it a riskier move.
Audio problem: As the ZZ top members are trying to convince Bobby about staying in school, there is a distinct microphone error after Frank speaks. When he says "and the presidents", you can hear it quite distinctively. It is as if he spoke too close to the microphone at the end of his sentence.
Continuity mistake: While Hank is reminiscing about the car with his father he is in the garage and does not realise he is being filmed by the cameras. The following scene, the filming crew is watching the footage in the truck and the shot shows the camera angle is now different and would only be possible if Hank was standing in the alley outside his house.
Continuity mistake: Peggy's sitting on the couch in her teacher's garb. Yet moments later when she and Bobby rush outside she's back in her usual outfit.
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.