Continuity mistake: Whilst Bobby is talking to the other caddy about the ice blocking, Bobby is holding a coned ice cream in his hand. You can see he is holding a napkin around the cone below his fingers. In the following shot that shows a close up of his Bobby's face the napkin has moved up and is under his hand.
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: 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: 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.
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.
Other mistake: Whilst Bobby is sitting on the bench at the baseball game you can see his shirt is yellow. When Bill is having his little temper tantrum, a shot of the field shows the pitcher is wearing a green shirt. Some of the other players were wearing blue. I doubt there was more than 2 teams or more than two different uniforms.
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.
Deliberate mistake: After Peggy has knocked King Philip off his horse at the end you can the sun is setting behind her, when it goes to a reaction shot of Bobby and Luann in the stands, it is a blue sky and sunny behind them. The following shot of Peggy it goes back to the sun setting. The mistake could be said to be deliberate as the shot was used earlier in the scene and probably used again to save time and money than re-animating the exact same shot.
Deliberate mistake: In the scene where Hank is mowing his and Minh's (Khan's wife) lawn he mows straight across from Minh's lawn to his own lawn. This would be impossible as in every episode including this episode (before and after this scene) there is a fence separating his house and Khan's house. It was likely removed to simplify Hank's going back and forth between the two ladies as they try to gain his affection with food and beer.
Continuity mistake: As Kahn is putting the golf club away after Hank has just used it there is a groove in the locker to support the club. Kahn seems to place the club horizontally in the locker no where near the groove and to the left of it. The next shot its now sitting in the groove vertically.
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.
Continuity mistake: Hank, Bobby and Peggy are eating at Sugarfoots. On their table, there is a mayo container. Peggy starts talking, and then it shows a close-up of Hank. Then there is a shot of the table again. This time, there is a mustard bottle in the same position and shape as the mayo. The mayo is gone.
Continuity mistake: The door to the slaughterhouse (which Luanne blocks with the barrel) changes configurations between shots. When Trip is trying to get in, the exterior is blue with a doorknob. After Peggy busts in, it is white with a pushbar across the middle. The interior is white with a pushbar in all shots.
Continuity mistake: While Hank and his friends are watching the game, right before Bill says, "Yes! Made it to the commercials!" he wipes his hands on the couch and leaves a mess on it, but when he is imitating the football player's touchdown dance, you can see that the mess is gone.
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.
Plot hole: As Dale comes to Hank's work and talks to Hank about the gun incident he has a spray pack on his back that is filled with poison and by accident sprays Joe Jack. Yet in the episode "The Exterminator" Dale was told by the doctors that he would not be able to use any type of hazardous chemicals with bug spraying as his lungs wouldn't be able to handle the fumes any more. Even if he ignored the advice the chemicals would have at least incapacitated him or killed him.