De-Kahnstructing Henry - S3-E13
Continuity mistake: When Kahn drives up the alley, passing Hank, Bill, Dale and Boomhauer drinking beer, there are no door handles on either the front or back door in the close-up of his car, yet, oddly enough they appear later on in the wideshot.
De-Kahnstructing Henry - S3-E13
Continuity mistake: When Peggy is returning the blue bowl to Minh she is holding the bowl and is outside the glass sliding door at Khan's house. The shot then shows Minh and goes back to Peggy where she is now standing inside the house and didn't move at all during the shot of Minh.
De-Kahnstructing Henry - S3-E13
Continuity mistake: When Kahn comes home after getting his promotion, Minh has the fridge door open. Between shots almost all the items in the door disappear, and the cans inside the fridge change colour.
The Wedding of Bobby Hill - S3-E14
Deliberate mistake: As Luanne is putting the dirt into Bobby's fruit pie you can see she rips open a large part of the packet. Yet in the next scene when Bobby is about to eat the pie there is no sign of where Luanne ripped the packet. Its likely this was deliberate as the joke in the scene was Bobby and Luanne's constant attempts to get back at each other, if they had left the large hole its likely Bobby would have not fallen for Luanne's prank.
The Wedding of Bobby Hill - S3-E14
Continuity mistake: During the scene where Peggy and Hank are enjoying a spa, Hank fills up the champagne glasses with beer. He stops pouring a bit before the top of the glasses and there is very little foam on the top. In the very next shot both their glasses have foam overflowing from it.
The Wedding of Bobby Hill - S3-E14
Revealing mistake: During Rad's haircut from Luanne, there is a shot that shows the both of them in the mirror. You can see both their reflections and the room in the mirror but the objects on the counter in front of Rad have no reflection.
The Wedding of Bobby Hill - S3-E14
Continuity mistake: As Bobby visits Connie and is at her window he lays his hands on the window sill. The next shot they are back by his side and they keep alternating back and forth even though he never moves them between shots. At the end of the scene Connie shuts the window smoothly even though his fingers were still there in the shot before.
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.
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.
Continuity mistake: After the dolphin encounter, Hank has water dripping his face. In the very next shot when the camera guy is talking to him and Luanne, the water suddenly stops dripping. The shots were too quick for it to stop that suddenly.
Continuity mistake: Whilst Hank is in the hardware store, there is a clock behind the clerk on the shelf. It changes from 7pm to 5pm between the later shots in the scene.
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.
Escape from Party Island - S3-E17
Continuity mistake: Before Hank & the old ladies depart Arlen, the guys (Bill, Dale and Boomhauer) are in the alley behind the van. The next shot they are against the wall and the van is opposite them in the alley.
Escape from Party Island - S3-E17
Continuity mistake: As Hank is driving, whilst trying to get off the island, a large Alamo beer display can drops in front of the van. In the next exterior shot you can see it actually drops again but to the left of the van.
Escape from Party Island - S3-E17
Continuity mistake: In the scene where Peggy is singing and Bill joins in, you can see his white singlet is clean. In the following shot of Bill it has a number of stains on it.
Love Hurts and So Does Art - S3-E18
Continuity mistake: After Hank fills up the ice trays and then throws them into the sink, if you look inside the sink you will see they are empty. A few moments later you can see the sinks are full of water without Hank or anyone else filling them up.
Love Hurts and So Does Art - S3-E18
Continuity mistake: As Hank puts up his football picture in the museum, he places it on the wall. Once he does there is now a pin holding it up at the top of the picture even though he never put a pin there.
Love Hurts and So Does Art - S3-E18
Continuity mistake: In the medical center as Peggy is filling out the forms there is a sign above Peggy's head. When the shot change to where Hank is taking Bobby into the doctor's office, the sign has moved to a bit below Peggy's head.
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.
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.
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.