Stupidity: An explanation is given for the reason why the bombs planted on the Gundam are not activated by remote control (they have plastic explosive in the regiment but not remote controls!), but no reason why they set the timer for the explosion to 30 minutes, way too much to be of any use in combat against the Gundam. Moreover, if the vulnerable spot of the Gundam shield were situated where it explodes at the beginning, it'd be completely useless.
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)
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.
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.
Stupidity: The Tomorrow People tend to enjoy walking into and walking out of most scenes rather than teleporting. In particular, when fighting and needing to run away, they'll teleport to get a better fighting vantage instead of teleporting out of the situation.
The Power of the Doctor - S13-E9
Stupidity: After the crew of the space train have taken out the Cybermen, the Cybermen begin regenerating, which one of the crew points out. This guy seems to be aware of how regeneration works, but doesn't shoot at them again. In the series, it has been shown that shooting someone during a regeneration cycle will kill them instantly, but this idea is never considered.
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.
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: After the accident, Dawn is in spirit form on the road trying to wave down an oncoming car (driven by Martha Kent). Dawn doesn't know she's a spirit that can pass through objects at that point. Since Martha can't see her, she keeps driving straight towards Dawn. Dawn sees the vehicle isn't slowing down and instead of simply stepping out of the way to avoid getting hit, she turns her back, revealing to the audience that objects can pass through her now.
Stupidity: "Rei" comes into the circle, having been champing at the bit to "turn him into a smear on the floor." She's wielding a sword, Kovacs is unarmed, and she...slices him a bit, instead of a quick killing blow.