Character mistake: Hank seems surprised to learn a lot of the Alamo's defenders weren't from Texas. Given that kids study this in American history, especially Davy Crockett's role in the historic event, it seems unlikely he'd be ignorant about this.
Continuity mistake: In this episode only, Hank admires his father and defends, or dismisses, most of Cotton's bad qualities. As Peggy says: "You just cannot see your father for who he is." Throughout the rest of the series, Hank and Cotton's relationship is tense and unpleasant. In the episode "The Father, The Son, and JC" (Season Six), Bobby can't even find an old photo in which Hank and Cotton are both happy.
Character mistake: Hank talks about watching the Broncos vs the Cowboys in Super Bowl XIII. This is incorrect. They played in Super Bowl XII. Super Bowl XIII was the Cowboys vs the Steelers.
Megalo Dale - S7-E10
Continuity mistake: Chuck Mangione is shown living in the Mega Lo Mart, having faked his death after the explosion. Yet, he was shown in "Death Of A Propane Salesman" at Buckley's funeral.
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 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.
Continuity mistake: The entire episode is about Hank being very attached to his current truck, and refusing to purchase a new one (until he has no choice). But in S4 E23 Hank tells Peggy "You know how much I want a new truck."
Character mistake: Hank says that his parents haven't spoken in four years. However, Cotton and Tilly were both at the Hill home in the episode "Nine Pretty Darn Angry Men" (Season 3). Cotton bullied Tilly on that occasion. And four years has not passed in between those episodes, or else Bobby would be a high school student.
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.
Square-Footed Monster - S13-E3
Continuity mistake: While Hank is at Arlen City Hall, asking about forms for a legal petition, the first clerk tells him that Hornsby has been dead for 11 years. The filled directory board is visible on the wall. However, when the second clerk says Hornsby has been dead for 18 years, the directory board is entirely blank.
Square-Footed Monster - S13-E3
Continuity mistake: When the four "day laborers" hop into Eric's pickup, then stop at Mrs. Dwyer's house, there is no doorknob on the door in the wide shot. However, a doorknob appears in the next closeup.
Square-Footed Monster - S13-E3
Continuity mistake: When the McMansion starts breaking apart, endangering the other homes, Dale's watch is on his left wrist, as usual. But when the neighbors arm themselves with tools, Dale's watch is on his right wrist (it's not a flipped shot), then it returns to his left in the next shot.
Square-Footed Monster - S13-E3
Continuity mistake: While the neighbors are tearing down the McMansion with their tools, when Hank chainsaws the door and kicks it in, Hank's watch suddenly vanishes from his wrist mid-shot.
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 mid-air is missing. The animation is incomplete at the left side of the screen.
Character mistake: Genealogist is misspelled as "geneologist" in this episode.
Bystand Me - S10-E2
Continuity mistake: When Bobby encounters Harv at the Get In Get Out mini-mart, Harv's fingerless gloves vanish and reappear a few times until Bobby leaps into Dale's van. (00:11:00)
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.
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."