Continuity mistake: When Leanne first arrives, she kisses Luanne, and gets red lipstick marks on her. Later, when Leanne and Luanne are near the bathroom and Leanne says "I knew you would understand" (about Bill), she kisses Luanne, but there are no marks from her lipstick. Even if she mostly kissed Luanne's neck, at least part of some of the marks should show when Luanne turns to leave (after talking to Peggy).
Continuity mistake: After the Mother's day recital the Hills are driving home in the truck. When they show Bobby saying, "Uh I didn't take my medicine" you can see the seat backing behind him is a dark green color. You can also see the framing and bars around the back window is also dark green. After showing Peggy and Hank again, it goes to another close up of Bobby and the seat backing is now light blue like the front seat backing. The framing and bars around the back window have also changed to a silver color.
Continuity mistake: When Hank and Bobby throw toilet paper over Junie Harper's tree, Hank is only able to throw one roll over the tree and after Bobby knocks over the birdhouse they have to run away. The next morning when Hank is driving Bobby they look over to see Junie Harper trying to get the toilet paper out of the trees, but there is now a lot more than just one roll.
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.
Continuity mistake: When Buck tells his employees about his plan for "service with a hug" there's a closeup of Hank. In the next shot a car pulls up in front of Strickland Propane, and in the exterior shot the front door knob is at the right side of the door, but in the next interior shot the door knob is still at the right side of that door, though it should be on the left side. (00:03:45)
Continuity mistake: While Hank and his friends are watching the game, right before Bill says, "Yes! Made it to the commercials!" he wipes his hands on the couch and leaves a mess on it, but when he is imitating the football player's touchdown dance, you can see that the mess is gone.
Continuity mistake: The sliding glass door at the Hills' house leads into the kitchen. On the wall next to the door is the chore list and a cutout of the state of Texas, and sitting on the floor is a trash can. There is also no sign of the kitchen table which sits right inside that door as well. Sometimes a trash can is there, etc. When Hank storms out of the house while rest of the family is opening presents, there is a shot when Peggy comes out after him and it shows back inside the door. Instead of what is normally on the wall to the right if you were looking from the outside in, you see a small dresser and all the wall looks to be either a picture or a mirror.