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: In the original, the knight of the Phoenix suddenly appeared during the arena fights interrupting the show and stealing the Gold Cloth. In this remake of the saga, Sienna/Saori Kido leaves the arena by plane during a bombardment that occurs way before Nero/Ikki arrives to steal the Cloth. There is no reason why she would fly off in her VTOL without bringing the Golden Cloth with her, then (there's a lot of time for that). Instead she leaves it for the 4 Saints for them to "protect it", against a whole army and on foot in the middle of the desert.
Stupidity: Xander really has no reason not to believe Buffy when she tells him that Miss French is evil/a giant bug. There is an in-universe explanation of pheromones affecting him, but that's flimsy at best. He's already dealt with vampires and witches and body-swapping, and there has already been a murder around the time Miss French showed up... the fact he doesn't believe Buffy seems very forced and contrived.
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.
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: 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: 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.
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)
Siege Protocol: Part 2 - S3-E12
Stupidity: This team never packs enough ammo. The two little skirmishes they were in maybe consumed 120 rounds each x8 guys makes 1060 and that's pushing it. A soldier's combat load is 7 magazines, 210 rounds each for their primary weapon system. These dudes should have at least 3 mags each left, and Seals being Seals fighting far from the main force always pack more ammo, at least 390 rounds. There's a Seal training video where Seals are doing a centre peel drill and it says they pack 4000 rounds for 8 men. (00:49:15)
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.