Deliberate mistake: Hank only discovers the tattoo on the back of his head after having his hair shaved off. There is no way, however, he wouldn't have noticed it before this. The tattoo artist had to shave hair off the back of his head before putting on the tattoo. While he might have not realised right away, the pain the following day and the fact that he would have noticed a large part of his hair missing would make it unavoidable.
Deliberate mistake: Why wouldn't Hank just use a credit card to cover the outstanding payment he owes on his insurace? It was established in the episode Rich Hank, Poor Hank that Hank has an emergency credit card and could easily use that and would be covered immediately. His panic over not having insurance would outweigh any problems he might have with using his credit card and the fact that he is dealing with an insurance company there is no conceivable way they wouldn't accept a credit card or ask if he has a credit card to cover the payment. The mistake seems to be deliberate as it sets the story up for Hank going somewhat over the edge with protecting the house.
Deliberate mistake: When Dale calls Hank from John Redcorn's trailer, the wooden clock behind Hank (in the Hill's kitchen) has no markings or hands to tell what time it is. This is a mistake as it is the exact same shape and object as it was before this episode and I doubt they replaced the clock with an completely exact object as before. A side note on the mistake is that it may be considered deliberate as the clock in previous episodes is shown frequently in the background and will generally change between shots.
De-Kahnstructing Henry - S3-E13
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. (00:15:30 - 00:16:40)
Deliberate mistake: As Dale is taking photos of Bobby's ventriloquist doll you can see he is taking the photo from the upper right of where Bobby is standing in his house. However the angle of which he takes the photo from would be impossible as it's to the left of their screen doors and there is no window or see-through material from that angle.
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.
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: The Olympic symbol (of 5 inter-connected rings) is upside-down on the tracksuits the torch carriers are wearing near the end of the episode. It has 3 rings at the top, not 2.
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.
Won't You Pimai Neighbor? - S4-E18
Deliberate mistake: Before Bobby takes the final spiritual test, you can see Connie is behind Bobby with her parents. When Bobby starts looking at the objects she has moved over to the right of Bobby nowhere near were her parents were before. This would have been deliberate for when he's taking the test he picks Connie in the mirror and this would have been impossible to do if she was right behind him.
Deliberate mistake: Luanne gets pregnant at the end of season 10 and gives birth in this episode. However, despite the passing of several months being implied through various storylines in the interim, she does not have a pregnant belly until this episode. The rest of the time her stomach was as flat as it usually is.
