Deliberate mistake: Hank only discovers the tattoo on the back of his head after having his hair shaved off. There is no way, however, he wouldn't have noticed it before this. The tattoo artist had to shave hair off the back of his head before putting on the tattoo. While he might have not realised right away, the pain the following day and the fact that he would have noticed a large part of his hair missing would make it unavoidable.
Plot hole: Amazing that neither Hank's mother nor father ever saw the bandage on the back of his head, peeled it off, and would discover his tattoo.
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.