Continuity mistake: After Connie tells Hank she is experiencing her first period, Hank consults the book that Connie's parents left for Hank. There is a close up of the folder from Hank's point of view and you see there are not many pages on each side. You can tell this as you can see the binder's covers below the papers on each side and there is not much material on either side. The next shot that shows Hank skimming through the papers each side of the folder has a lot more papers on each side than the previous shot.
Hillennium - S4-E10
Continuity mistake: Before Peggy reads Luanne and Bobby her musing about "Noel", Bobby is to her right and the shot shows them all from behind. The next shot he is to the left of Peggy and right next to Luanne, despite Luanne having Peggy and Bobby between her at the start of the scene.
Won't You Pimai Neighbor? - S4-E18
Continuity mistake: At the beginning of the episode, Kahn gives the guys in the alley invitations for his Pimai party. As Dale opens his invitation he places the envelope in front of the invitation he is holding. The next shot they have reversed position with the invitation in front.
Rodeo Days - S4-E12
Continuity mistake: Whilst Bobby is first talking to the rodeo clown, the guy in the red shirt has some red paint under his nose. When the angle changes and shows both clowns the red paint has disappeared.
Hillennium - S4-E10
Continuity mistake: After taking some propane tanks from work, Hank comes home and starts telling Peggy to throw out her old computer. The clock in the background starts off at 10 o'clock. Hank then sees Dale knocking at the door and the time has changed to 1:50. After Dale comes in, it changes again to about 11:35.
Continuity mistake: Bill picks up the case of Metalife products to put them in his car. After discovering he has a blister he picks up the box and the logo on the box is facing the left-hand side. The next shot it's changed to the front of the box. The change of shots was instant so there was no chance he could have turned the box around.
Continuity mistake: When Hank goes to buy an "L pipe" at the Mega Lo Mart, his truck is parked in the middle of the parking lot and nothing in between the middle of the cars. As Hank is about to leave in his truck there are concrete blocks ahead of his car (with a sidewalk next to them). Also if you look at the car behind Hank's truck before he is about to leave it is a white color. Whilst he is reversing it is now a dark blue color.
Won't You Pimai Neighbor? - S4-E18
Continuity mistake: As Hank and Bobby are leaving the reverend's office, Hank puts his hands on Bobby's shoulders and is at an angle away from the reverend. In the next shot from the reverend's angle we can see he is facing her and the position has changed from the previous shot.
Peggy Hill: the Decline and Fall (2) - S4-E1
Continuity mistake: When Peggy is drinking the formula for breakfast, she has a small napkin placed over her neck cast. As Peggy and the baby start crying the napkin has disappeared.
Won't You Pimai Neighbor? - S4-E18
Continuity mistake: When Hank looks at his invitation he reads the writing in it. The next shot you can see the writing on the card as if Hank had turned the card over pointing towards the ground. However there was not enough time between shots for him to have turned it around.
Continuity mistake: In the scene where Bill is trying to open the beer can with the back hoe, he rips up the pavement with it. As Hank sees the mess he gets in the machine and pushes the pavement back that Bill tore up. When Boomhauer comes along you can see his foot falls into the hole and gets stuck even though Hank pushed it back. Also if you look the soil Bill dug up has disappeared when Boomhauer comes along.
Continuity mistake: When Bobby & Peggy are about to steal Bill's flag, the truck drives right up against the flagpole. In the next shot Bobby is standing next to the flagpole and there are a few changes. The first is that the truck has a bit of space between the back of it and the pole, whilst the first shot it had no space in between (as it hits the pole). The other change is where the rope is knotted on the pole. In the first shot it was on the opposite side of where Peggy was standing. The next shot she has not moved but the rope is right next to Peggy facing her.
The Perils of Polling - S4-E25
Continuity mistake: Luanne's penguin puppet is on her right hand, then her left hand within a shot.
Bills are Made to be Broken - S4-E3
Continuity mistake: When Hank and Bill are sitting on the hood of Bill's car and talking, one shot of the football field shows it to only be about 70 yards long between the end zones.
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.