Plot hole: After the old guys take Hank's clothes & throw him over the fence at the Alamo, Hank goes right into the building without having to unlock the door. Despite the fence being locked up, it seems a little odd that such an historical monument like the Alamo wouldn't have its main door locked.
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.
Character mistake: Hank seems surprised to learn a lot of the Alamo's defenders weren't from Texas. Given that kids study this in American history, especially Davy Crockett's role in the historic event, it seems unlikely he'd be ignorant about this.
Character mistake: Hank says that his parents haven't spoken in four years. However, Cotton and Tilly were both at the Hill home in the episode "Nine Pretty Darn Angry Men" (Season 3). Cotton bullied Tilly on that occasion. And four years has not passed in between those episodes, or else Bobby would be a high school student.
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.