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: In this episode wily old battle genius Jean-Luc Picard and amazingly smart human-android Dahj act exactly by the definition of stupidity of this website ("something daft, like running upstairs with a killer behind them, instead of out of the front door"), and even surpass it, because the killers are not even chasing them yet. And why not? Because they are in a public area with a ton of people in the middle of what is basically the capital of the world; no band of kidnappers would attack at that point, or at least, it's way more unlikely. But from there, our nearly centenarian hero (steps away from official government buildings and in a world with communicators, teleports etc.) goes up a ramp of stairs leading to a desert rooftop with no exit and no witnesses, exactly where a group of evildoers would attack - and are even able to cover their tracks up exactly because of this choice. (00:31:50)
Stupidity: Towards the end of the season, the Borg Queen uses Soong to get control of the ship. When asked by the heroes who gained back control, she says that her plan is to get back to the Delta Quadrant and prepare for the Confederation that she already fought in her 'future'. If that's her plan, it's quite silly; she prepares for a conflict she might lose, when she has in her grasp the man who, as she knows, will originate the Confederation itself; Soong, not to mention that she can assimilate (or destroy) the whole Earth already. No reason is given why she'd let 'us' live and thrive.
Stupidity: Adam Soong's daughter is a grown woman who is well aware of her unique critical condition and the outside world, and is homebound because of her health condition that prevents her from being exposed to direct sunlight and pathogens. Apparently, with all the free time she has and awareness and investment in her father's researches who are all about her, she never ever looked at her father's computer (which has all the info about her story right there on the desktop) nor googled him before.
Stupidity: The Chateau is stormed by the Zhat Vash commandos. The two trusty housekeepers prepare to fight the aggressors armed to the teeth by grabbing... a bread knife and a wine bottle. All is good, since the bottle is super-effective, knocking down a Romulan wearing a helmet. This absurdity aside, moments later during the fight it turns out that the valets had weapons stashed everywhere in the room, even strapped underneath tables! Why would they start off with such ineffectual weapons instead of reaching for the guns, other than of course for dramatic purpose?
Stupidity: From a remote location, Kore deletes her father's research data from his computer, defeating him. So Adam Soong in a few decades of work as a geneticist, apparently never once backed his work up or kept a hard copy of it. (00:20:05)