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.
Through the Valley of Shadows - S2-E12
Stupidity: Burnham and Spock find one person alive from the otherwise-dead crew, miraculously. They know Control can infect humans, they know how advanced it is, the entire setup screams "trap", and yet they don't even question whether Gant even might be under Control's...well, control. A simple scan would have turned up anomalies and they could have avoided what followed.
Stupidity: Nora's dad believes in heaven and doesn't want to upload himself, because he wants to be reunited with his wife. When visiting Lakeview, he tells Nathan that Nathan's soul went to "real heaven," so he's just talking to a simulation. Which means there's no reason he can't upload himself. His soul will go to real heaven like he wants to, and he can leave a simulation behind for his daughter to be with. Everyone would be happy, but nobody makes that argument.
The Perks of Not Being a Wallflower - S1-E3
Stupidity: Superman finally smashes the weirdly strong bad guy through a wall, then goes to Lois, says "he's gone", and whisks Sarah to hospital. But he has no idea if the bad guy is "gone" or not - they've just had an epic fight, he has some sort of super strength / resilience, and for all Superman knows he'll come around in 10 seconds and finish the job of murdering Lois.
Suggested correction: Superman knows the 'strong bad guy' is close to his own strength. After fighting him, he knows what effect the crash through the wall would have had on him, if he was knocked out, and how long he would be out for. So he knew there was little risk of the guy coming around in 10 seconds. Alternatively, he X-ray scanned the area and saw the guy was no longer there.
A Bad Reflection on You - S1-E38
Stupidity: The decision to risk revealing their identities to Bulk and Skull is one that the Rangers could have easily avoided. Since they tell the bullies to cover their eyes and ears, under the false pretense of a magic trick, they could have simply teleported to the Command Center, or any other secure location, and then morphed, well away from prying eyes.
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)
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: Some ancient advanced civilization took to the task of building this amazing net of stargates that enables instantaneous traveling over hundreds of light years or more, but any stargate can be disabled by anybody just by covering it with dirt or rocks. Apparently if the stargate is buried then it becomes inactive. See Season 1 EP.1.
Suggested correction: This is just you having a different opinion on how the Stargates should work. In fact, the ability to make a Stargate inactive by burying it is a brilliant move by the Ancients. Burying the gate, or even creating a barrier, prevents enemies (like the Goa'uld) from having a convenient way of invading a planet. Although some races, like The Nox, show the ability to activate a Stargate without having to form an unstable vortex.
Stupidity: The last remaining Xindi, in desperation, attempts to release the virus over the fan, despite the virus not being fully ready. However, it seems the only reason he didn't release the virus at that time was he had to seek cover from Archer and T'Pol shooting at him and to start shooting back at them. However, he had plenty of cover from the rooftop stairwell, which was right next to the fan, and he had enough time to dump out the contents over the fan.
Infestation - S1-E3
Stupidity: So "Dr. Smith" runs into her sister's boyfriend on the Resolute and pushes him into an airlock when he figures out who she is. The door immediately closes and a countdown to purge the airlock ensues. Who would design an airlock to do that? What if someone went in there by mistake or was doing some maintenance on it? To make it worse, there's no override inside the airlock? It's located in the corridor.