Continuity mistake: Peggy's shoes go from purple to white in one shot in Nancy's kitchen.
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.
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.
Plot hole: Amazing that neither Hank's mother nor father ever saw the bandage on the back of his head, peeled it off, and would discover his tattoo.
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.
Continuity mistake: Peggy's sitting on the couch in her teacher's garb. Yet moments later when she and Bobby rush outside she's back in her usual outfit.
Love Hurts and So Does Art - S3-E18
Plot hole: There's no reason Hank or Peggy can't call the deli owner and tell him not to sell any more food to Bobby once he contracts gout.
Suggested correction: Bobby has generally earned his parents' trust. He might get into trouble occasionally, as many pre-teen boys do, but not so much that Hank and Peggy need to cover all the bases. They believe that he stopped going to the deli. As Peggy tells Connie, "He is doing everything he can to get back on his feet in time for that dance."