Continuity mistake: When Herrera is swinging the fire in the trick for Nancy's birthday party, you can see Dale, Nancy and John Redcorn are at their tables sitting near the stage. In some of the following shots you can see they are further back, towards Hank and Peggy.
De-Kahnstructing Henry - S3-E13
Continuity mistake: After Kahn shows the guys his new car, he shows off his new sunroof too. Later when Kahn goes to Strickland propane and in the establishing shot it shows his car outside the store and the sunroof is no longer on his car and no marks to indicate its just closed. (00:01:00 - 00:02:00)
Continuity mistake: In past seasons, Hank's truck has obviously been shown as a 1992-era Ford Ranger,however in this episode it is shown as a 1980's-era Ranger.
Continuity mistake: During the first (or the second) Board & Zoning meeting, there is a jug of water next to Nate. In the wide shots of the board the handle is to the left but in the close ups of Nate it's now facing the right.
Continuity mistake: As Peggy comes to see Bobby about how his essay is going, there is a pad and pen next to him on the bed. The next shot Peggy sits down next to him which was where the pad and pen were on the bed. She then reaches for the pad and pen from behind Bobby. She never makes any movement before or after she sits down so there is no way she put the items would go to being behind Bobby.
Deliberate mistake: The Olympic symbol (of 5 inter-connected rings) is upside-down on the tracksuits the torch carriers are wearing near the end of the episode. It has 3 rings at the top, not 2.
Continuity mistake: After Hank calls Bobby into the room to talk about the woman's magazine Peggy discovered, you can see Peggy's hair is a little messed but nothing in it. A few shots after Hank asks Bobby about making the turkey there is a close up shot of Peggy and she has a few stains in her hair which disappear in the next shot. The stains look very similar to the ones she gets a little later on when she falls on the turkey.
Continuity mistake: When Dale knocks John Redcorn the shape of the lamp he's holding changes between shots. The shape you can see changes between the shot of Dale knocking him out and the next shot that shows a wide shot of the people in the room. The other mistake in the shot is when Dale drops the remaining part of the lamp. Despite dropping it from about chest height the remaining part doesn't break when it's dropped.
Love Hurts and So Does Art - S3-E18
Continuity mistake: At the start of the show when Joseph is tying up his bike it is a green color. As the girls leave and Joseph starts talking to Bobby it changes to a blue color. Then Joseph starts to ride his bike and it changes back to being green.
Other mistake: After Hank & Peggy pick Bobby up from the airport you can see part of the clouds through the windshield. One of the clouds you can see stays in the exact same spot whilst they are driving along the main road in the back windshield. It is a cloud because of the distinct color. It also couldn't be a sticker as you can see when they park the car at the restaurant there are no marks on the windshield.
Love Hurts and So Does Art - S3-E18
Continuity mistake: When Bobby is showing off his injured toe at school and doing a Q & A session, the pillow below his foot is white but in the next shot it is blue.
Rodeo Days - S4-E12
Continuity mistake: Near the beginning of the episode when the Hill's are having dinner, you can see Hank's glass in the first shot is to his left. Next shot it's to his right.
Peggy Hill: the Decline and Fall (2) - S4-E1
Continuity mistake: Before Hank starts arguing with Cotton near the end of the episode, Cotton has a can of beer in his hand. When Cotton is being held by Hank and swinging his arms at Hank the can of beer has disappeared. There was no moment where we can hear him drop the can, and as he pushes Hank we never see him drop it.
Three Coaches & a Bobby - S3-E12
Continuity mistake: As the football team is meeting Coach Sauers for the first time, you can see the team from behind with Bobby kneeling and Joseph behind him to his right. However, when the shot shows the group from the front, Joseph is now to the left and some kid with brown hair to Bobby's right. (00:07:40)
Continuity mistake: When Dale is leaving for work and John Redcorn is coming up the walk, Dale locks at least four or five deadbolts on the door. But when John Redcorn uses his keys, there is only the regular doorknob lock.
It's Not Easy Being Green - S5-E16
Continuity mistake: As Hank tells Bill & Dale that they are going to drain the quarry (whilst in Dale's basement) and Dale lets his burning cigarette drop. Dale & Bill start to freak out and it goes to a wide shot of the three of them & the cigarette Dale dropped is not on the ground anymore.
Won't You Pimai Neighbor? - S4-E18
Continuity mistake: In the scene at the "Get In, Get Out" shop, Connie and Bobby's drinks have each have a bendy straw. When Connie is walking off they have changed to normal straws as you can see the marks of bendy straws have disappeared.
Continuity mistake: As Bobby is complaining about the capers, we can see there is almost a full jar of them. After Luanne shows the old clothes she is wearing to work, the jar is near empty. Later in the scene the jar returns to near full again.
Continuity mistake: During the scene in which Bobby shares his Hungryman dinner with the raccoon,the food in the left of the tray is a white color. As the shot shows the raccoon eating, it's bright yellow.
Continuity mistake: In the shot where Hank is using the paint roller on Bobby's wall, where he has it positioned it is around level with his head. When the shot changes to showing his face the roller has moved considerably higher out of position from his face.
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.