Stupidity: After talking to the bartender, Calleigh goes back the lab and talks to Caine, and he wonders if they got a false positive from the vic's blood alcohol. Calleigh then gives a detailed description of how that could happen; Caine already knows how (obviously this was done for the audience, to explain it, but in the context of the show, it makes no sense).
Stupidity: When Kellin is hit with the neurolytic emitter, it erases her memories of the outside world. However, the effects aren't immediate and take some time (enough to get her to sick bay and have time to talk to Chakotay). However, she spends her time telling Chakotay to help her remember their relationship, etc. when her memory is gone instead of just making a recording of herself describing the relationship and her feeling which can then be shown to her after her memory is gone. She might not believe the recording, but seeing herself discuss the situation would be better than just relying on Chakotay (who will soon be a stranger she never met) telling her something so unbelievable.
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.
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: Medusa is the queen of the secret kingdom on the moon. She knows that they are very secretive and keep hidden from the humans on Earth who would have no idea who she is or that there are secret people on the moon. And yet in Hawaii, she walks up to an ATM and tries to demand by voice commands it give her money, saying, "I am Medusa of Attilan, and I need money." It is extremely stupid of her to think a random ATM in Hawaii would know who the secret queen of a secret moon base is.
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)
Stupidity: Donna runs in to save everyone from the collapsing pylon, dying in the process, despite the fact that Superboy or Raven, both more powerful/resilient, could have stopped it falling without any issues whatsoever. Not even like anyone was distracted - the fight was over, they were all just standing around.
Stupidity: One of Rogue's defining character traits is her inability to have physical contact with another person because of her powers and the sorrow it causes her. Several episodes of this show, however, featured devices that could suppress mutant powers, the inhibitor collars being the most prominent. Despite this technology at their disposal, they never even think to have Rogue wear an inhibitor device for times she would like to touch someone. Even if she didn't want to wear those specific collars, a character like Beast or Forge could easily create a new and harmless device by reverse engineering and adapting the existing ones. This of course would eliminate Rogue's ongoing dilemma and potentially curb her development as a character, but it doesn't make sense from the standpoint that she longs for physical contact with others.
Stupidity: When the bad guys are discussing the plans inside a private jet, the scene finishes and there's a shot of the plane in the sky. The plane immediately veers to the right, and spins almost 90°, as fighter jets do when they turn quickly. If there were three people inside, (one of whom was in the bathroom) they would have been thrown about the cabin quite violently. (00:11:25)
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.
Blade VS Buffy Summers - S12-E10
Stupidity: Blade fights several vampires for a minute or two, and then pile drives the Asian lady vampire into a table. Only then does he decide to throw a UV bomb up into the air to kill all the vampires in the room. He should have led with that! Wiped them all out from the start, and by not doing so, he gave plenty of vampires time to escape. (00:19:06)
What If... The Watcher Broke His Oath? - S1-E9
Stupidity: Ultron says he can destroy galaxies with a thought. So regardless of Dr. Strange's protection spells, he could destroy the planet they're all standing on, or evaporate the atmosphere, leaving them all suffocating in space, and just step away from the fight entirely while they die.
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.
Recognition - S1-E17
Stupidity: After fighting Wootox in Sky's body, why didn't Cruger contact the other Rangers and inform them about the body switch? This would have spared everyone a lot of trouble.
The Passion of Conner - S1-E28
Stupidity: For some strange reason, Conner powered down from Triassic mode before battling Zeltrax.
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.
Stupidity: Why did Nadira decide to rewire Circuit instead of simply destroying or dismantling him? If she decided to simply destroy him, then Ransik and his army would have been victorious against the Power Rangers.
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.
Yomigaere! Eiyuu Densetsu - S1-E1
Stupidity: Despite being in training for 6 years at the temple to compete for a magical armor consecrated to a constellation and meant to harness the power of the Cosmos, Cassios and everyone else but Marin (Shaina towards the end) are mistified about the whole idea when Seiya uses it. What in the world have they all been training for, for 6 years, then? Shaina has to be the worst trainer ever. Cassios even calls it a 'superstition', but his master Shaina channels the power perfectly. It's like a Muggle working at Hogwarts and not believing in magic.