Stupidity: The super powerful Romulan commandos (no doubt with the help from the higher-ups infiltrated in the Federation) managed to touch up the footage of the fight in the roof so to remove every trace of the Romulan agents present. But Picard has been running, dodging blasts, ducking, and is knocked back by a huge explosion caught on camera and not deleted; we see it in this episode and it is unequivocally not caused by him. What is the point of going through subtly deleting every trace of the aggressors when it is transparent that something real happened and it's not all Picard's imagination? And the police simply take Picard back home from San Francisco to France without questioning him, not caring about investigating the explosion in the heart of the city involving a famous Admiral battling invisible enemies. If the conspiracy can erase anyone from the tape, why not erase Picard too, or the explosion and explain how he ended up K.O.'d differently?
Stupidity: When the new principal is addressing the student body, Avalanche tries to impress Kitty by causing a couple of small earthquakes, one of which causes the scoreboard to crash to the floor below. The principal laughs off the incident and continues to address everyone instead of either evacuating the area or having everyone take cover.
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: Characters repeatedly make note of how hard to kill the Wraith are, but sometimes, especially in the final episode(s) of season 1, they go down easily in a few bullets each, and then don't even regenerate as the characters turn their attentions elsewhere.
Stupidity: When Lois, possessed by Dawn, comes downstairs and says she's going to the prom and Clark is taking her, Clark doesn't think for a moment it could be Dawn. He already knows Dawn can posses others, those people don't act like themselves, Dawn is obsessed with the prom, Lois isn't acting like herself, and Lois is now not only suddenly prom obsessed for no reason, but wants to go with Clark when she said that would never happen.
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.
Hanging with Axel: Part 2 - S3-E5
Stupidity: Hassleberry and Jesse sneak around Axel to free Syrus from the tree whilst Axel is distracted with the duel. They are trying to be discreet whilst Axel is distracted, but Hassleberry shouts "Hey, Sarge. Open up a can of Neos on this guy" to Jaden, even though Axel would definitely hear this. (00:06:38)
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.
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: 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 Night of the Firebrand - S3-E2
Stupidity: West is introduced to, then knocked unconscious by Vixen as she hides a club behind her back. A trained Secret Service agent like West would not have let his guard down in this situation, as the entire fort was awash in bad guys.
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.
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.
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.
Storm Before the Calm: Part II - S1-E38
Stupidity: Shane could have easily avoided the blast from Lothor by simply flying away to dodge it. Instead, he just hovers over him and allows his Battlizer to be destroyed.
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.
Emohawk - Polymorph II - S6-E4
Stupidity: On the walk back to Starbug, the Emohawk jumps on Lister's head to disguise itself as Lister's hat, but it leaves itself in its natural form whilst the crew continue to walk. The Emohawk is supposed to be disguising itself to fool the crew into making them think it is any everyday object. The Emohawk eventually changes into Lister's hat, but leaving itself in its natural form even for just a small amount of time could blow its cover. (00:18:15)
The Tale of the Dream Girl - S3-E10
Stupidity: A boy walking through the bowling alley stops and lets Johnny pass, even though Johnny is supposed to be a ghost no one can see.
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)