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.
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.
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.