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)
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."
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)
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.
De-Kahnstructing Henry - S3-E13
Continuity mistake: When Hank walks into Luly's men's room, Hank's watch is on his left wrist, Kahn's hair is parted on his right side, the stalls are to Hank's right and urinals to Hank's left (same side as his watch). Some of the following shots show them in the mirror's reflection. After Kahn says, "Times hard, but Minh's a fighter, they be ok," it cuts to a particularly odd shot of Hank and Kahn. The entire bathroom we see behind them is backwards, as if it's the mirror's reflection shot (stalls and urinals on the opposite sides), but Hank's and Kahn's watch and hair part are on the correct sides, which is not possible if it were a reflection. (00:19:10)
De-Kahnstructing Henry - S3-E13
Continuity mistake: When Minh is sitting on the ground surrounded by trash bags, the door is visible behind her, minus one doorknob. By the time Peggy sends Hank to the rescue, the doorknob reappears.
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 Hank and Kahn are together in Luly's men's room, there is a good view of the bathroom's walls, ceiling etc. Beside the door there are only six rows of tiles between the wall and floor, there is no molding at the top of the wall, and so on. A bit later, there are at least seven rows of tiles, and suddenly there is crown molding between the ceiling and wall, and so forth. (00:19:00)
Love Hurts and So Does Art - S3-E18
Continuity mistake: Whilst Hank is trying to take the painting off the wall from the gallery, the artist has his hands by his chin. As Hank is being dragged away in the following shot, the artist is being held up by a guy behind him. Its too quick for him to have changed positions that quickly and looks like part of the scene must have been deleted as the change is too large to have been missed.
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.
Take Me out of the Ball Game - S3-E24
Continuity mistake: As Bobby slides into the girl scout's box of cookies with his bike, there is a lock box (to the right of the desk) and some cookies on the desk (to the left of the desk) and are spread apart from each other. A few shots later when you see the desk again they are now side by side.
Take Me out of the Ball Game - S3-E24
Continuity mistake: After Peggy loads the bases in the final game after a wild pitch strikes one of the women, you can see her hair is blonde. In the next shot when Mr. Strickland comes to see Hank the girl who got walked has brown hair and in a ponytail. The woman went straight to first base, plus there was not enough time between shots for a pinch runner to replace her.
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
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.
De-Kahnstructing Henry - S3-E13
Continuity mistake: At Strickland Propane, when Kahn hands Hank his propane tank, it is set down on the counter right beside the bell. However, in the shots facing Kahn, the bell is directly in front of him, but the propane tank is nowhere to be seen. Additionally, during this scene note the difference in the ceiling height in relation to the wall boards and the doorway behind Hank. (00:02:20)
Nine Pretty Darn Angry Men - S3-E7
Continuity mistake: In the previous episode "Peggy's Pageant Fever", Hank feels bad that Peggy enters the pageant only to win the new white pickup truck. At the end when things are going wrong he paints his truck white to please her. It's back to red in the next episode.
Three Coaches & a Bobby - S3-E12
Continuity mistake: When Hank sees Coach Sauer driving his car on the field, you can see Sauer's car has a red front bumper. When we see the front bumper again a few shots later it is grey. (00:15:30)
Three Coaches & a Bobby - S3-E12
Continuity mistake: If you look carefully during Coach Sauer's training run while Bobby is running down the stands, you will quickly see the mud disappear on Bobby's face and reappear in the next frame. (00:08:35)
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.