Continuity mistake: In the scene where Bobby is refusing to partake in thanksgiving celebrations and Hank starts asking him whether he's nervous about the turkey carving. You can see Bobby's carving knife is pointed toward the wall with the blade (curved edge) pointed towards Bobby. Before Bobby picks it up to give back to Hank its facing the other way.
Continuity mistake: After the banquet dinner where Bill sees Lenore, she comes to visit him at home. They are sitting down on the couch and when she's talking she has her hand on his chest and you can see there is a pen in Bill's right shirt pocket. Between shots she talks about stealing Bill away at the prom and in one quick shot the pen disappears and the next shot it returns. Also look at Lenore's hand in this scene. It goes from being next to his chest, away from his chest back to being on his chest.
Continuity mistake: As Hank visits Cotton to give his uniform, Cotton goes into the middle stall of the bathroom. If you look at the stall to the right it has its door open and no one is in there. As they are speaking you can see the door has closed in the reflection of the mirror. You can see even see it's closed without using the mirror when Hank puts the uniform down on the chair.
Continuity mistake: As we see the float for the time in the driveway when Cotton arrives home, the float is vertical to the driveway. In the following shot Peggy starts asking Cotton for his war medals, the float is now turned around horizontally to the driveway.
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.
Continuity mistake: As Hank and Bobby are leaving the reverend's office, Hank puts his hands on Bobby's shoulders and is at an angle away from the reverend. In the next shot from the reverend's angle we can see he is facing her and the position has changed from the previous shot.
Continuity mistake: Before Hank starts arguing with Cotton near the end of the episode, Cotton has a can of beer in his hand. When Cotton is being held by Hank and swinging his arms at Hank the can of beer has disappeared. There was no moment where we can hear him drop the can, and as he pushes Hank we never see him drop it.
Continuity mistake: After taking some propane tanks from work, Hank comes home and starts telling Peggy to throw out her old computer. The clock in the background starts off at 10 o'clock. Hank then sees Dale knocking at the door and the time has changed to 1:50. After Dale comes in, it changes again to about 11:35.
Continuity mistake: As Bobby slides into the girl scout's box of cookies with his bike, there is a lock box (to the right of the desk) and some cookies on the desk (to the left of the desk) and are spread apart from each other. A few shots later when you see the desk again they are now side by side.
Continuity mistake: When Peggy is returning the blue bowl to Minh she is holding the bowl and is outside the glass sliding door at Khan's house. The shot then shows Minh and goes back to Peggy where she is now standing inside the house and didn't move at all during the shot of Minh.
Continuity mistake: During the scene where Hank is talking to Bobby in the garage about the baby, Hank is wearing brown shorts and sitting on a stool. When Hank stands up you can see the top of his pants are now blue, the same color as his usual pants. When Bobby passes in front of him, he has brown shorts on again.
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.
Continuity mistake: When the family leaves for the basketball game Peggy brings the wrong foam finger (not the basketball one) so Hank turns around to get it. It shows him walking into the house, finding it but also finding what he thinks is laundry all over the floor. He also hears what he thinks is innocently the washer or dryer running. He follows the noise towards the kitchen, slowly opens the door to find his mother and Gary presumably having sex on the kitchen table. The problem here is that the kitchen has no door. From inside the kitchen in any episode it is never visible. I checked and further into this episode while opening presents it shows an entrance to the kitchen from the living area where Hank entered and there is no door on that side either. In truth it is an open doorway.
Plot hole: As Dale comes to Hank's work and talks to Hank about the gun incident he has a spray pack on his back that is filled with poison and by accident sprays Joe Jack. Yet in the episode "The Exterminator" Dale was told by the doctors that he would not be able to use any type of hazardous chemicals with bug spraying as his lungs wouldn't be able to handle the fumes any more. Even if he ignored the advice the chemicals would have at least incapacitated him or killed him.
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.
Plot hole: Hank finds Dale and Bill in the hole and as he's rescuing them Hank says, "Well you haven't moved in about 50 hours?" Hank found out they were missing when the guy who rented the backhoe comes looking for it and Hank is surprised to find they have gone missing. Seems a bit odd no one noticed them missing or decided to report it over 2 days. Whilst Bill lives alone and maybe no one would have noticed, Dale's wife (Nancy) and son would have noticed after that length of time. Despite Nancy still having an affair with Redcorn, there is too much evidence throughout the show's history that show both she and Joseph were constantly concerned when anything happened to Dale.
Factual error: During the scenes where the Hills arrive at the airport in Japan, there is no flight crew outside or around the terminal when they exit. Whilst they may be the last people to exit the plane, there will be one or more crew members to farewell passengers and also to close the terminal door. There doesn't seem to be any crew anywhere close, which seems particularly odd especially as Hank and Cotton manage to just stroll back onto the plane. A little after they leave the camera crew just go right through the terminal onto the plane without anyone there to stop them.