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.
Hillennium - S4-E10
Continuity mistake: Before Peggy reads Luanne and Bobby her musing about "Noel", Bobby is to her right and the shot shows them all from behind. The next shot he is to the left of Peggy and right next to Luanne, despite Luanne having Peggy and Bobby between her at the start of the scene.
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.
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.
Revealing mistake: Whilst Bobby is reversing the truck before hitting the flagpole in Bill's yard we see the driveway in front of the truck. The very next shot shows Peggy from behind the truck instructing him how far to go to the flag pole and you can see they have used the same background as the shot before from the other angle. You can tell this as both shots are the same background as both angles despite from different viewpoints are exactly the same items and objects in both shots. Added to this there is a driveway in each shot, and Bill doesn't have 2 driveways in his backyard.
Continuity mistake: When Bobby & Peggy are about to steal Bill's flag, the truck drives right up against the flagpole. In the next shot Bobby is standing next to the flagpole and there are a few changes. The first is that the truck has a bit of space between the back of it and the pole, whilst the first shot it had no space in between (as it hits the pole). The other change is where the rope is knotted on the pole. In the first shot it was on the opposite side of where Peggy was standing. The next shot she has not moved but the rope is right next to Peggy facing her.
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.
Rodeo Days - S4-E12
Deliberate mistake: When Bobby is trying out for the cattle roping at the rodeo, he gets the rope tightly around the calf's neck. As the calf starts to drag Bobby you can see the rope is now very loose around its neck. A little later when the clowns are chasing each other the rope is back tightly around the calf's neck. May be deliberate as it may look like the calf would have been choked with the rope being so tight around its neck.
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.
Audio problem: When Buck is trying to frame Hank for the murder of Debbie, he uses a hidden tape recorder to try and incriminate Hank. However the tape recordings are not the same, as they don't match up with each other. In the scene he says, "Yes I was angry. Debbie threatened to tell my wife that we had sexual relations". Later on the Sheriff is playing the tape back to Hank and the tape says: "(Small Pause) Debbie threatened to tell my wife that we had sexual relations". The tape doesn't match up on a few things. First the second recording takes a quick second before Hank starts talking despite in the first recording he said "Yes, Yes I was angry. Debbie." and no pauses in between these lines. Secondly Buck says at the end of the first recording "I got all I need" immediately after Hank finishes speaking and then he stops recording. In the second recording after Hank finishes speaking the tape keeps playing but we don't hear Buck speak.
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.
Continuity mistake: At the beginning of the episode there is a shot of the parked vehicles and the Hill's car is yellow (the car next to Dale's van). As Bobby and Connie are talking, the car behind Bobby (the Hill's car) is now blue.
Plot hole: As the guys are checking out the vacant house inside, they are surprised to see it has a pool. However the problem with this is its right next to the driveway in the front of the house, in the open with no fence in front of the driveway so it would provide a clear look through from the alley. As they state they never noticed it in 18 years living there, yet walking up and down the alley it's a bit hard to imagine being that open and they never saw it. Even the final shot (aerial shot) at the end of the episode we see it was far too obvious for them to have never seen in that space of time.
Continuity mistake: When Luanne gets home from work at the start of the episode, Bobby is waiting for her to get the food she brings home. She puts the duck shaped bag on his tray with the beak of it facing Bobby. The next shot its facing the other way.
Continuity mistake: When Peggy is insulting Bill to try and get him to sell Metalife products again, he has a beer in his left hand. In the next shot when he tries to convince Peggy to give him another chance the beer has disappeared even though he never put the beer down. They were outside on the front lawn so there was not enough time for him to hide it or place it somewhere else on his front lawn.
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.
Continuity mistake: When Peggy tries to sell Dale the Metalife products she is just passing the fence (at the bottom of her driveway). In the following shot we her cart is in the middle of the road. The change of shots there was not enough time for her to have made that distance from the end of the driveway to the middle of the road.
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.
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.
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.
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.