Firefly, Light My Fire - S1-E1
Stupidity: The button Benita uses to open her trap door also turns on/off the record player and swings the record arm.
Norman Mailer, I'm Pregnant! - S5-E6
Stupidity: Luke arrives at Lorelai's house. He comments that she left her car light on. Lorelai then tells him that she left it on because the porch light is out. He says that the battery is going to die. She tells him that she has it timed out perfectly. She then says that there will be 2 hours to spare and that the car has all day to charge. Cars don't charge unless they are running. Is she really going to run it all day? Why didn't Luke point out the error in her logic? Doing so is staying true to the character. The oversight is glaring.
Stupidity: When Richie and Fonzie swap clothing and walk in for The Duel with the Frenchman (both with faces covered to conceal their plan), the whole audience watching The Duel gasp and are all surprised to learn they switched places. But, before the switch was revealed, Richie (as Fonzie) walked in with a nerdier style walk and Fonzie (as Richie) walked "cooler" and looked much more in shape. Also, the head covering Fonzie wore was sheer and you could still see his face, but everyone was STILL fooled.
Stupidity: Aunt Bee learns that a New York writer and his wife have moved to Mayberry and she invites him to speak at a Literary Club meeting which will be held at her home. By telephone, Aunt Bee gives directions to the writer's wife. She says, "We're a quarter mile outside of town" - but she neglects to say in which direction.