Bills are Made to be Broken - S4-E3
Continuity mistake: Whilst Bill is practising football in Hank's yard there is an aerial shot that shows Bobby & Hank walking towards Dale & Boomhauer and are close to them. In the following shot they are quite a bit further away from their previous position. Also the position of Dale & Boomhauer next to the garage changes between shots.
Peggy Hill: the Decline and Fall (2) - S4-E1
Continuity mistake: In one scene Hank is helping Peggy scratch one of her arms that is in a cast with some normal straws joined together. At first he is holding the last and first straws and there is only a few straws. The next shot he is holding the straws with one hand about halfway down (2-3 straws down) and there are more straws then there was before. After this shot the straws revert back to how it looked originally.
Continuity mistake: As Peggy & Bill are checking into the hotel, there is a wide shot of the lobby and Peggy is wearing a sleeveless shirt. In the next shot that is a close up and she is wearing a pink full sleeve shirt.
Hillennium - S4-E10
Continuity mistake: As Peggy goes for her present and rips the wrapping paper to see it's a grandfather clock, it is set at 12:35. The following shot it's at 11:55. A little later on when Hank is about to varnish the clock, the time changes again before and after he closes the garage door where he is doing the varnishing.
Won't You Pimai Neighbor? - S4-E18
Continuity mistake: After Bobby takes the first spiritual test, Minh and Kahn come behind Bobby. Looking at Minh's hair and the top of her dress are both very wet. However before this she was completely dry and there was no scene where water was sprayed on her. She stays wet for the rest of the scene probably indicating that there is a scene deleted from the episode as it is far too obvious to be missed.
Continuity mistake: As Kahn is yelling at Bobby after he sees him kissing Connie over the fence he chases after Bobby and in one of the shots you can see the ladder Bobby used is gone. The following shot it shows Luanne in the bathroom and through the window we see the ladder has reappeared. The other change in the shots is the ladders and their size. Before the shot in the bathroom the ladder's height (Bobby's ladder) was enough it reached over the fence. As we see the ladder through the bathroom it's not even reaching the top of the fence.
Hillennium - S4-E10
Continuity mistake: Just before Hank uses the varnish on the grandfather clock you can see a quick shot of the power drill. This would have been impossible as we saw, and he told Bobby, he got rid of all his power tools the day before for some corn. Later in the scene when he wakes up the power tool has disappeared for good.
Continuity mistake: After Peggy has fallen out of her wheelchair she had her bag on the back of her wheelchair. When Cotton is taunting her and pushes the chair near her, the bag has disappeared.
A Beer Can Named Desire - S4-E6
Continuity mistake: After Bill kisses Rose on the tombstone you can see he has quite a few sweat stains visible on his shirt. Bill then goes inside the house looking for Rose and the stains have disappeared.
Little Horrors of Shop - S4-E4
Continuity mistake: During the scene where Peggy is taping a photo of Hank to the blackboard to discuss about the substitute teacher of the year. When she tapes it up you can see it's near the top of the board near the writing accompanying it. After a shot of the students the photo has moved down quite a bit along with the writing that was there.
Continuity mistake: As the plumbers are installing Hank's new low flow toilet, the guy with the red hair stands up and is at level height with his co-worker standing next to him. In the next shot he is now a few inches taller.
Continuity mistake: Luanne in one scene tells Hank a man asked if she would like to join the mile high club and when she tells him she is facing Hank. In the next shot she is standing in the same position but has turned around and is facing away. There was not enough time for her to move between shots.
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.
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.
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.
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: 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: Whilst the guys are waiting in the alley for Hank to get back (before Boomhauer leaves) you can see the backhoe is behind Boomhauer. When it changes to showing the empty street from their point of view, the backhoe is now down the street. The following shot its back to behind Boomhauer.
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.