Continuity mistake: Hank says that when he and Peggy were 18, they were already married. But in the season one episode "Square Peg", Peggy tells Luanne that she "never even kissed" a boy until she was 20.
Continuity mistake: When Bobby is trying to convince Hank's friends to join the abstinence club, and when he asks Boomhauer he just stays silent. Bill then signs up and gets one of the cards Bobby has. As Hank starts to talk it goes to a close up of him but in the next shot Boomhauer is looking at one of the cards. Bill still had his card so where did Boomhauer get one of those cards?
Continuity mistake: As Luanne is becoming a "Born again" virgin, she yells after being dunked in the water. She yells "I'm a Virgin." and there is a shot to the left of two guys in the distance playing Frisbee look behind to their left. The shot sees them from the left meaning they were to Luanne's left. A few shots later Luanne is getting out of the lake and one of the guys who was playing Frisbee comes up to her from her right side and the other guy follows him. There wouldn't have been enough time in the scene for them to get all the way over to the right side of the field and not much reason to either.
Continuity mistake: In the episode where porn videos are being sent to Hank, there is a close-up shot of a machine printing out address labels for Hank's house. These labels say 320 Rainey Street. However, in this episode, when Peggy is looking at the mail, all of their mail has 84 Rainey Street as their address. In several other episodes, the address is stated to be 123 Rainey Street.
Continuity mistake: After the frantic phone call from the hospital, Hank rushes to the emergency room. In the hallway there are two doors, the one to his left says "Consultation" whilst the one to his right says "Examination". He uses his left hand to open the door and in the next shot you can see the door now says "Examination" and "Consultation" on the opposite door.
Continuity mistake: When we see Bobby talking to Hank about the allergy test there are lots of black marks (dots for the allergy test) on Bobby's back and one red circle around one of them. As Hank is looking at them there is a shot from behind Bobby and the red circle has gone.
Continuity mistake: When Peggy says that Bobby could have invited her and Hank to the dog house, Hank says that they wouldn't have been able to fit in the door, but he went in and out of it earlier while fixing up the doghouse. At the end of the episode, Peggy is inside the doghouse with a student she is tutoring.
It's Not Easy Being Green - S5-E16
Factual error: Boomhauer's car, Ms. Sally, has a Texas flag license plate on it. These plates were not issued until 1992, but Ms. Sally was driven into the quarry in the late 70's or early 80's.
It's Not Easy Being Green - S5-E16
Continuity mistake: When Hank goes to Bobby's class for "environmental court" and is sworn in, you see Bobby sitting at a large desk and to the right there is nothing next to it. The next shot there are now a few empty desks next to the large desk.
It's Not Easy Being Green - S5-E16
Continuity mistake: As Hank tells Bill & Dale that they are going to drain the quarry (whilst in Dale's basement) and Dale lets his burning cigarette drop. Dale & Bill start to freak out and it goes to a wide shot of the three of them & the cigarette Dale dropped is not on the ground anymore.
It's Not Easy Being Green - S5-E16
Continuity mistake: When Hank, Dale & Bill go to the quarry to get the car, they use a tow truck to try and pull it up. If you look at the tow truck you can see it is a red color. Later on when the protesters come and are sitting in a circle and singing the tow truck is now orange. It stays orange for the rest of the scene.
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.