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.
Slave Island - S1-E7
Stupidity: At the beginning of the episode, Pyro is among the Genoshan prisoners, and he is wearing his flamethrower device. While his inhibitor collar will suppress his mutant power of pyrokinesis, he can still use the flamethrower itself as a weapon. This would be akin to a prison allowing an inmate to walk around with a loaded gun. (00:02:12)
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.
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: 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: 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: 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.
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.
Day 4: 12:00 A.M.-1:00 A.M. - S4-E18
Stupidity: After leaving the power plant to pursue the terrorists and retrieve the nuclear football, Jack orders the helicopter to take out the first Jeep. After he realises parts of the football are missing, why does he not order the helicopter to pursue and take out the other Jeep, preventing any further trouble from Marwan? (End of season 4's story, most likely).
Invasion of the Punk Frogs - S2-E8
Stupidity: Shredder uses a holographic projector to appear as a normal person. He could have just taken off his armor.
Stupidity: While flying over the jungle in the Dragonfly, Dr. Quest uses the Dragonfly's speakers to tell the Po-Ho tribe he is their Air God and is angry for the tribe taking hostages. While he was at it, Quest should have ordered the Po-Ho's to release the hostages.
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: With about 5 minutes left, the Black Sheep fly towards a Japanese carrier. They are flying Japanese planes. The Japanese spotter speaks in Japanese. The translation on the screen says "There ours" instead of "They're ours."
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: During a raid of a Latin stash house, Hailey and Kim find two girls with a pistol. In Spanish, they say no bullets. Kim interprets what the girls say and Hailey replies, l didn't know you spoke Spanish. Makes no sense that a partner on an elite police unit in Chicago would not know a member of the team speaks Spanish. (00:14:58)
Magical Express Murder Case: File 2 - S2-E11
Stupidity: Kindaichi and the others are called up by Satomi, who is one of the performers, so they can be in attendance for the show. They don't get changed, but somehow they are so late for the show that they are the last people to arrive, and the show is already ongoing and displaying the most famous act. If Satomi warned them late, makes no sense that he wouldn't be in the theater to begin with.
Stupidity: The inspector knows that his house has been bugged; he does not know how many bugs and cameras are there, he just knows there are some. He does find a bunch of them with great ease when he gets back home - making you wonder how could he have ignored them to begin with, since all it takes is for him to raise his eyes, they are fairly big black cameras who do not camouflage at all for the most part. He then proceeds to make a phone call to the big baddie from his landline. Nobody in their right mind would do such a thing. Heck, you wouldn't want to use your home phone for such a call even if you didn't know that someone just put bugs all over your house.