Take Me out of the Ball Game - S3-E24
Other mistake: When Peggy strikes Bill in the head in the softball game, he gets hit on the left side of his head. Later in the scene he is using an ice bag on his head but he's icing the other side.
Square-Footed Monster - S13-E3
Other mistake: When Lucky drives off in the pickup with the tow chain, as the McMansion crumbles to the ground, Luanne runs away from the house, and part of her legs are missing. The animation is incomplete.
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.
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: 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.
Redcorn Gambles with His Future - S9-E11
Other mistake: In the season four episode "Nancy Boys", when Nancy calls John Redcorn and tells him that she wants him back, he says, "I'm thirty-six years old. I don't need this crap." But here while John is talking to Hank, he mentions waking up one day and realizing that he is forty. If four years had passed since his break-up with Nancy, then Bobby and Joseph would now be sixteen and at least sophomores in high school, but they are still in middle school.
Square-Footed Monster - S13-E3
Other mistake: During the storm, after Peggy uses the axe on the McMansion support beam, when it cuts to Luanne running with the tow chain attached to Lucky's pickup truck, note the other end of the chain in midair is missing. The animation is incomplete at the left side of the screen.
Other mistake: When Hank tells John Redcorn that his family is not Jewish, John is noticeably surprised. However, in the episode "Revenge of the Lutefisk" (3x21), John was at church with the Hills and Gribbles. He already knew that they are not Jewish.
Other mistake: The reflecting light on the water is on the wrong animation layer, appearing over anything else in the scene that comes into their position, despite being in the background. (00:20:40)
Other mistake: At Kahn's barbecue, everyone likes the burgers he cooked on his charcoal grill. Peggy is among the people who crowd around the grill. But in the episode "Hank and the Great Glass Elevator", Peggy and Bobby are shocked when they eat a burger that Luanne cooked with charcoal.
Serves Me Right for Giving General George S. Patton the Bathroom Key - S13-E15
Other mistake: Here, it's made into a big deal that Cotton wants to be flushed in the same bathroom Patton used. Yet in Season 4, Episode 2, "Cotton's Plot," he successfully gets a cemetery plot in a Texas military cemetery.
Bad Girls, Bad Girls Whatcha Gonna Do - S7-E3
Other mistake: When Bobby is caught spray-painting the fence, Hank says that he and Peggy took their wedding photos in front of that fence. In the episode "As Old As The Hills", part one, there is a photo of Hank and Peggy living in an apartment after they got married.
Transnational Amusements Presents: Peggy's Magic Sex Feet - S4-E23
Other mistake: Hank is scraping his grill after grilling and charcoal briquettes can be seen in the propane grill. (00:07:38)
Other mistake: At the prison, Bill meets Alicia, the same woman who gave Leanne a ride to the Hill house in Season Two ("Leanne's Saga"). Same voice, tattoo on the arm, and general appearance. Alicia tells him that she was in prison for killing her boyfriend. So it's odd that she was free in Season Two. Most likely, a sentence for homicide or manslaughter would be at least five years, and that much time has not passed. Otherwise, Bobby, Connie, and Joseph would be in their late teens.
Other mistake: When Boomhauer sees Katherine at the gas station, she says, "It's been twelve years." When Hank talks to Boomhauer in his garage, he mentions Boomhauer breaking up with Katherine twenty years ago.
Other mistake: The premise of this episode makes no sense. Bobby and Connie have previously spent a lot of time together and/or with Joseph. They were also shown on "dates", i.e. the high school dance where No Doubt played. Basically, they were a steady junior high/middle school couple. However, in this episode, they are suddenly "too different" and can barely get through a few dates together.
Other mistake: In this episode, Peggy is terrible at gardening. In the fourth season, she brought flowers to the man who was making foot fetish videos. She said that the flowers were "so pretty" and were from her "own garden."
Other mistake: Dale laughs at Nancy for picking up the diazinon, instead of the bird repeller gel. He then picks up a bag, goes up the ladder, and when he turns the bag around, it says diazanon on the bag he picked up. The only gel in the scene was what Nancy picked up.
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.