Stupidity: The entire plot hinges on a military facility that knows it's housing what's essentially a sentient world-ending disease, and that has the foresight and resources to build a containment room with a cyanide failsafe, having nothing else to stop said virus from breaking out beside the glass her room is mostly composed of. Once she's out of that room, she just has to run through an unlocked, labeled exit door and hop a fence. Where are the emergency bulkheads? Where are the armed guards watching the hallways? Why isn't that fence electrified? Why isn't she wearing a metal shock-collar at all times? Even if that glass was bulletproof and/or they seriously underestimated her strength, they'd still have to open the door to her room at various times to give and take her food, books, laundry and waste.
Stupidity: In the scene with the water-jug puzzle, both Zeus Carver and John McClane initially suspect that the small carrying case contains a bomb. McClane goes ahead and opens the case, which confirms that it is a bomb (the electronic readout in the case even says: "I AM A BOMB. YOU HAVE JUST ARMED ME"). If they suspected it was a bomb in the first place, why didn't Carver and McClane immediately try to warn the dozens of pedestrians all around them to evacuate the area before McClane opened it? That would be a seasoned police officer's first instinct. Instead, McClane and Carver banter and bicker and never attempt to warn the public, even as the timer is ticking down.
Stupidity: Why would 006 put Bond in a self destructing helicopter instead of just shooting him? Being Bond's old partner, he of all people should know how good of an escape artist Bond is.
Stupidity: In the opening robbery, killing the third guard made no sense. Even if they didn't kill anyone, they'd still already committed a serious crime, that would result in lengthy prison time if caught. It makes no sense that they have no problem leaving witnesses when they're guilty of armed robbery, but don't want to when they're guilty of murder. If they didn't kill the third guard, their chances of getting caught would've been the same as if they didn't kill anyone.