Continuity mistake: When Allabaster is chasing Hank in his car, he loses the front left hubcap from his car. Just as they go over the speed bump if you look at Allabaster's car when it is in the air for a brief second you can see the hubcap is back on the tyre (more visible in slow motion). Later we see the tyre again and the hubcap is off for the rest of the scene.
Continuity mistake: When Peggy & Hank are talking about Tammy whilst in bed, there is an outside shot of the house with light streaming out of one of the windows (the master bedroom). Yet when we see Peggy & Hank inside their room the blind for that window is down, making it impossible for the light to stream out of the window like it does.
Continuity mistake: When Peggy, Hank, and Tammy are in the car and Peggy says "We all make mistakes", her lipstick is a duller, orange shade, then it goes back to being red.
Continuity mistake: When Peggy and Hank are looking the mirror, as Peggy says "We look like a couple of movie stars", her hair is its normal reddish-brown color, but her reflection in the mirror has lighter, more dull brown hair.
Continuity mistake: Hank says that when he and Peggy were 18, they were already married. But in the season one episode "Square Peg", Peggy tells Luanne that she "never even kissed" a boy until she was 20.
Continuity mistake: When Bobby is trying to convince Hank's friends to join the abstinence club, and when he asks Boomhauer he just stays silent. Bill then signs up and gets one of the cards Bobby has. As Hank starts to talk it goes to a close up of him but in the next shot Boomhauer is looking at one of the cards. Bill still had his card so where did Boomhauer get one of those cards?
Continuity mistake: As Luanne is becoming a "Born again" virgin, she yells after being dunked in the water. She yells "I'm a Virgin." and there is a shot to the left of two guys in the distance playing Frisbee look behind to their left. The shot sees them from the left meaning they were to Luanne's left. A few shots later Luanne is getting out of the lake and one of the guys who was playing Frisbee comes up to her from her right side and the other guy follows him. There wouldn't have been enough time in the scene for them to get all the way over to the right side of the field and not much reason to either.
Continuity mistake: In the episode where porn videos are being sent to Hank, there is a close-up shot of a machine printing out address labels for Hank's house. These labels say 320 Rainey Street. However, in this episode, when Peggy is looking at the mail, all of their mail has 84 Rainey Street as their address. In several other episodes, the address is stated to be 123 Rainey Street.
Continuity mistake: After the frantic phone call from the hospital, Hank rushes to the emergency room. In the hallway there are two doors, the one to his left says "Consultation" whilst the one to his right says "Examination". He uses his left hand to open the door and in the next shot you can see the door now says "Examination" and "Consultation" on the opposite door.
Continuity mistake: When we see Bobby talking to Hank about the allergy test there are lots of black marks (dots for the allergy test) on Bobby's back and one red circle around one of them. As Hank is looking at them there is a shot from behind Bobby and the red circle has gone.
Continuity mistake: When Peggy says that Bobby could have invited her and Hank to the dog house, Hank says that they wouldn't have been able to fit in the door, but he went in and out of it earlier while fixing up the doghouse. At the end of the episode, Peggy is inside the doghouse with a student she is tutoring.
It's Not Easy Being Green - S5-E16
Continuity mistake: When Hank goes to Bobby's class for "environmental court" and is sworn in, you see Bobby sitting at a large desk and to the right there is nothing next to it. The next shot there are now a few empty desks next to the large desk.
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.
It's Not Easy Being Green - S5-E16
Continuity mistake: When Hank, Dale & Bill go to the quarry to get the car, they use a tow truck to try and pull it up. If you look at the tow truck you can see it is a red color. Later on when the protesters come and are sitting in a circle and singing the tow truck is now orange. It stays orange for the rest of the scene.
Continuity mistake: After Peggy throws the tomato at King Philip you see it lands on the badge on his jacket. Most of the tomato lands about the top of his badge and seems to set on the top part. A few scenes later when Peggy is being put in the stocks for punishment you see Philip again and the stain has moved down the badge. Most notably the tomato stain looks larger and a large chunk of it has moved below the badge onto the shirt.
Continuity mistake: When Hank and the family are approaching Cotton's table at the rummage sale, there are two empty knife sheathes and one sheathed knife on his table. In the next shot, there are 3 sheathes and 2 knives out of the sheathes. (00:03:25)
Continuity mistake: When Hank's trying to convince his dad to let the Vietnam vets join the VFW, the table behind him with the bowl of fruit and the vase of flowers on it disappears between shots. (00:12:45 - 00:13:15)
Continuity mistake: When Hank's trying to convince his dad to let the Vietnam vets join the VFW, the table behind him with the bowl of fruit and the vase of flowers on it disappears between shots. (00:12:45 - 00:13:15)
Returning Japanese (1) - S6-E21
Continuity mistake: On the plane whilst Bobby is watching the TV in front of him, you can see a man to the left of Bobby and an empty seat to Bobby's right. The seat arrangement looks to be like the middle row of seats where there is 3 seats instead of two. After the shot shows footage for the "Haiku" movie the shot changes to Bobby and the man sitting next to him but there is now no empty seat next to Bobby. It appears that he is now sitting at a window seat.
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.