Stupidity: Whilst Reva is running across the rooftops, there is a moment where she does a backflip in order to propel her forwards towards the next rooftop. If she was attempting to jump between roofs, then doing a backflip would not have been useful as it would only slow down her momentum instead of build it. (00:25:28)
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.
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: 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 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: 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.
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: 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.
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: "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.
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.
A Rough Whimper of Insanity - S1-E7
Stupidity: The hacker's VR goggles are not plugged in to anything (despite having a wire for this purpose) when he and Tom sit down at the computer in the teacher's house.
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.
The Power of the Doctor - S13-E9
Stupidity: When Yaz finds the huge Dalek drill, she starts saying everything she is thinking aloud, commenting "They're already here. Seismology. Volcanoes. Daleks, and the Master. This is not good news." There is absolutely no reason for her to say this out loud, considering that she is completely alone and saying this could've risked her getting caught.
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.
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: In the flashback, Emily's sister takes ill while playing her flute. In the next scene, the sister is sick in bed and Emily now has the morpher around her neck, but she is in the exact same outfit. If the sister was forced to pass the legacy on due to disease, it should have taken more than just a few minutes or even hours to learn that.