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.
Continuity mistake: After Peggy throws the tomato at King Philip you see it lands on the badge on his jacket. Most of the tomato lands about the top of his badge and seems to set on the top part. A few scenes later when Peggy is being put in the stocks for punishment you see Philip again and the stain has moved down the badge. Most notably the tomato stain looks larger and a large chunk of it has moved below the badge onto the shirt.
Answer: In addition to Brian Katcher's response: it's supposed to be a joke that Dale is always suspicious about conspiracy theories, mysteries, etc, but he is "clueless" about his own wife having an affair. Of course, as Brian wrote, many fans think that Dale is pretending to be clueless because he doesn't want Nancy to leave him.