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)
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.
Take Me out of the Ball Game - S3-E24
Continuity mistake: The scene where Hank and Peggy are fighting to control the pancakes, Hank flips the first pancake. In the next shot he's moved onto the other pancakes but the 1st one is just like it was before he flipped it, despite not flipping it between shots.
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.
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.
When Cotton Comes Marching Home - S5-E5
Continuity mistake: As Hank visits Cotton to give his uniform, Cotton goes into the middle stall of the bathroom. If you look at the stall to the right it has its door open and no one is in there. As they are speaking you can see the door has closed in the reflection of the mirror. You can see even see it's closed without using the mirror when Hank puts the uniform down on the chair.
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.
De-Kahnstructing Henry - S3-E13
Continuity mistake: As Kahn is ringing the bell in Strickland Propane trying to get some attention the bell is right next to his hands. When Hank comes out there is a wide shot and the bell is now a short distance from Kahn's hand. The counter also changes size as you can see where it ends just to the left of Kahn but in the wide shot the counter runs from wall to wall. (00:02:00)
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.
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: 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.
Continuity mistake: At the end when Laoma is crying and hugging Bill, the tears on her face are on her cheeks. As she asks, "Wait, Astronaut who?" the tears are now just found near her eyes. As Bill explains, she has her hands on his shoulders. She then turns and the tears are not even in her eyes now.
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.
Continuity mistake: When Hank Hill decides to take his son, Bobby, to shoot a deer at a local recreational resort named La Grunta, Hank shows Bobby what is supposedly a La Grunta brochure, but the description at the bottom-right of the brochure states that the text therein is referring to the "Shropshire House Inn & Resort."
When Cotton Comes Marching Home - S5-E5
Continuity mistake: Before Topsy (Cotton's friend) & Cotton tie up the restaurant manager there is a quick shot that shows the sign on the door for the men's room. It has the symbol on it for disability access. However in one of the previous shots when Cotton tries to leave the restaurant the sign is the same but there was no wheelchair accessible symbol.
Megalo Dale - S7-E10
Continuity mistake: Chuck Mangione is shown living in the Mega Lo Mart, having faked his death after the explosion. Yet, he was shown in "Death Of A Propane Salesman" at Buckley's funeral.
Continuity mistake: The entire episode is about Hank being very attached to his current truck, and refusing to purchase a new one (until he has no choice). But in S4 E23 Hank tells Peggy "You know how much I want a new truck."
Death of a Propane Salesman (2) - S3-E1
Continuity mistake: When Peg is on the phone with Buck the wall telephone has a long cord, then she hangs up the receiver on the wall, but in the following shot both the receiver and its long cord are weirdly missing from the wall phone. (00:05:15)
The Year of Washing Dangerously - S10-E9
Continuity mistake: Peggy is looking out the kitchen window into the Gribble household, which is wrong. Khan lives on the kitchen side of the Hill household. The Gribbles live on the garage side.
Nine Pretty Darn Angry Men - S3-E7
Continuity mistake: When Peggy's shoe sole comes off, it comes off the right shoe, but in the repair shop she hands her left shoe to the cobbler.
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.