Other mistake: After Hank & Peggy pick Bobby up from the airport you can see part of the clouds through the windshield. One of the clouds you can see stays in the exact same spot whilst they are driving along the main road in the back windshield. It is a cloud because of the distinct color. It also couldn't be a sticker as you can see when they park the car at the restaurant there are no marks on the windshield.
Other mistake: In the episode, Hank's truck is destroyed when it gets stuck on the train tracks and a train smashes into it. Later on when Bobby is walking home by himself he finds the cover for the gear shift stick and puts it in his pocket. After a while Hank finds Bobby and Bobby gives him the cover and Hank puts it right on. Sounds fine. The only problem is that Hank has to screw the cover back onto the stick shift but doesn't have to remove any part of the previous stick. When the train hit the car, Bobby puts the cover right in his pocket and it would have had a bit of the stick left in it, as he had to screw it on. Its unlikely Bobby would have removed the bit of stick inside it because when we see him pick it up there is no part of the stick he would have been able to grip to unscrew it from the cover.
Other mistake: When Hank runs into the building to hide and lays down in the square of moonlight on the floor, he looks up at the window and a couple of clouds pass by. The clouds move too quickly, and when Hank is shown again, no shadows from the clouds move across him.
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.