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.
Stupidity: At the start of the episode, the Brunnen-G planet is about to be under attack by His Shadow in a big ship that is capable of destroying the surface of the planet and everybody on it in under a minute with its fire power. It seems the Brunnen-G had time to respond, seeing as they send a counter measure against His Shadow... Except that they only send a single squadron of 6 fighters. Their planet is about to be obliterated by His Shadow's killer ship, and they only send up 6 fighters. And of course, they fail and all die except for Kai. (00:01:45)
Welcome to Hotel del Luna - S1-E1
Stupidity: The Mayor realises that Man-wol has approached him and taken out her rifle to shoot him with. Yet during the entire time she takes to aim the rifle at him and fire, the Mayor makes no attempt to flee the stage for his own protection. (00:38:15)
Stupidity: The master goes through all the trouble of making Luke the vessel so Luke can go and kill several people and risk getting the attention of the slayer, when all he had to do is have his minions go out and kidnap a bunch of people and bring them to him and he could've fed off them himself.
The New Original Wonder Woman - S1-E1
Stupidity: There's much fuss about who will take Steve Trevor back which is resolved via a contest. Why the Amazons don't heal him, if possible, then set him adrift to a safe port is never asked. They did this when Nazis invaded in the two part episode The Feminum Mystique.
Stupidity: In the original, the knight of the Phoenix suddenly appeared during the arena fights interrupting the show and stealing the Gold Cloth. In this remake of the saga, Sienna/Saori Kido leaves the arena by plane during a bombardment that occurs way before Nero/Ikki arrives to steal the Cloth. There is no reason why she would fly off in her VTOL without bringing the Golden Cloth with her, then (there's a lot of time for that). Instead she leaves it for the 4 Saints for them to "protect it", against a whole army and on foot in the middle of the desert.
Stupidity: The brothers are angry at Leo because they say he's responsible for them dying because he chose to save other soldiers instead of them, Leo also blames himself for the same reason and says he should have stayed and gotten them out. But in the flashback it shows Leo helping them and then running off to help other soldiers, after he runs off the brothers are killed just a few seconds later. Even if Leo had chosen to stay with the brother he couldn't have gotten them out in time, the only difference would have been Leo would have died with them, but Leo dies in the same war so he didn't live much longer. Leo's guilt and the brothers' blame don't make any sense at all.
Worlds Apart - S1-E2
Stupidity: The bad guy kills the deputy in the swamp, then later sees a little girl who witnesses the killing run away. He then searches the boat for a weapon and runs off after her after he finds a machete, without even considering the officer's gun still in its holster. Abby proceeds to make the exact same mistake later when she finds the dead officer (meaning there's danger nearby) and hears the girl screaming and runs in the direction of the screaming without taking the gun to protect herself.