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.
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: 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: Andor and Luthen set a vehicle to drive and distract the security team. The vehicle is destroyed, and they immediately round the corner in full view of the team on a speeder and drive away, then blow up the vehicle. They could have driven away on any number of other streets without revealing that they weren't in the vehicle, keeping their escape secret. And if they blew it up before the team looked too closely they might have even been deemed to have been killed in the crash.
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.
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: 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.
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.
Suggested correction: Superman knows the 'strong bad guy' is close to his own strength. After fighting him, he knows what effect the crash through the wall would have had on him, if he was knocked out, and how long he would be out for. So he knew there was little risk of the guy coming around in 10 seconds. Alternatively, he X-ray scanned the area and saw the guy was no longer there.
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: 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: On his own in his helicopter, TC earlier in the episode spots a very hard to catch area of vegetation where supposedly the color of the leaves is different from what's expected. However for the ending, with 4 people in the helicopter, everyone but Magnum misses a giant clearing with a bright red excavator in the open.
Stupidity: During the scene at the restaurant, Rose pulls the fire alarm. Then she and the doctor run through the kitchen, past several chefs who just duck and crouch into corners. This would easily be one of the stupidest ideas ever. If there was a fire, they would evacuate out the back door instead of just sitting there waiting to be choked to death. And if they knew about Auton Mickey, running out the back door would also be a lot more logical than just crouching down and waiting to be battered to death.
When in Rome - S1-E3
Stupidity: A supposedly covert camera is placed in plain sight on a wall in a crowded room, with a prominent antenna showing, and a blinking blue light. (00:16:55)
Stupidity: There's no way April would mistake Slash, his debut episode in Season 4, for one of the turtles as he's got spikes on his back, dressed differently too.
Stupidity: The Resistance is a rescue team that helps the various protagonists escape schools. They do this by leaving intricate hints that lead to a detour to the school alarm instead of going straight there, setting off the alarm and rescuing the protagonists.