Stupidity: Ahsoka is fighting against the spear-wielding woman. She keeps blocking the spear using both her sabers. It would be very straightforward to block the spear with just one lightsaber (as she proves she can do just as well after she loses the smaller one) and use the second one to, for example, cut off the woman's hands.
Suggested correction: This is opinion, not stupidity.
When in Rome - S1-E3
Stupidity: A supposedly covert camera is placed in plain sight on a wall in a crowded room, with a prominent antenna showing, and a blinking blue light. (00:16:55)
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: 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: After Bernie discovers a treatment for the infection, radiotherapy, everything goes back to normal. Except the contagion is airborne (which is why they were going to flush the entire ship's atmosphere), so they're just going to re-infect themselves in a few hours. And there's only one room on the ship that can be exposed to stellar radiation, so there's no way to clean the atmosphere either.
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.
Stupidity: The Resistance is a rescue team that helps the various protagonists escape schools. They do this by leaving intricate hints that lead to a detour to the school alarm instead of going straight there, setting off the alarm and rescuing the protagonists.
From Injustice Came the Way to Describe Justice - S1-E5
Stupidity: The police raid an apartment in search of guns. They should have used a ballistic shield for the point man to make entry and hit the apartment with a concussion device (flash-bang). The police officer who took a stomach full of lead would have more than likely survived had they been properly equipped. Ballistic shields have been around since 1977. This story takes place in 1992. (00:49:17)