Stupidity: Project Pegasus is a billion dollar structure with no security guards besides the couple dudes Fury shows the badge to at the entrance, no video surveillance, and once SHIELD arrives nobody has to even open a locked door anymore.
Suggested correction: First of all, Fury was allowed in as it's a government facility and he works for the government and as a SHIELD agent is allowed access. It's inside a mountain and they passed multiple security guards as they drove in, armed guards. Everything is thumb prints and cameras which was quite elaborate for that time. To say they lack in security is quite an understatement. SHIELD has quite some authority and can easily take control in the Pegasus project facility.
You are right about the main entrance being truly secure both for guards and strategic position. The problem is that they are free to just roam the facility for an hour, blast through doors, not a soul in sight, no evidence of camera monitoring the inside of the structure, and once the gag of the pad is finished, no door requires it. Actually, funnily enough you can see a guard of the place opening the elevator for Fury and the supervisor, as if the thumprint scan was needed to even get into the elevator itself, but Keller then just walks into the archive just fine (from a different door than the one Vers blasted). There are keypads to exit places (for instance the hangar, when the agents in pursuit break through the door you can see a keypad on the wall) but only when it's convenient (Vers and Fury walked through that same door with no problem, not to mention the fact that the whole stairs seem to have none, which is funny for a place that has keypads both sides of doors).
Stupidity: The X-Men depart for space on a vehicle not designed for space, for an incredibly dangerous mission they know nothing about (and none of them can survive in space at that point), but don't suit up for it in the slightest - and with Nightcrawler and Quicksilver's powers as they are shown later, it'd be easy to do it without wasting time. Not only that, but Xavier communicates with NASA to get the briefing only after the X-Men have already departed.
Stupidity: Despite the fact that the villains know exactly where Brogan is for the better part of the movie thanks to a tracer, and that they display constantly that they are able and willing to hit with bold military operations even to the point of hitting an urban area overruling law enforcement (apparently Clay has authority to do that too), Brogan is able to get undisturbed back in the US through his friend's plane. Considering he was officially marked as a rogue agent and killed 8 DIA operatives, it's hard to see how Baron's plane could ever land on American soil after a long intercontinental flight.
Stupidity: After making love, Selina notices Batman's scars. She surely was caught in the moment, but, it's something she really was bound to notice sooner. (00:53:10)
Suggested correction: She notices the scars on his back first, which are the worst of those on his body, this may well be the first time she sees his back.
Stupidity: The marines all wear helmets as part of their protective gear when they go into the Phobos compound, but Bennett and Akua do not wear any helmets at all. They wear bullet proof vests and arm themselves with weapons, but unlike the other marines, they go in without any way of protecting their heads.
Stupidity: At the very beginning of the movie, law enforcement is depicted executing a no-knock warrant. They approach a house surreptitiously and use a ram to open the door with no warning. When they arrived at the scene, all the cars and trucks in the raid were using flashing lights and wailing sirens. So much for the element of surprise.
Stupidity: Right before the movie's final battle, Sub-Zero taunts Cole with his wife's necklace and makes him chase him into a portal. Sonya was right next to Cole, and she did not come along with him. They had previously planned to take on Sub-Zero together, but apparently she just left him to chase Sub-Zero alone to an unknown location.
Stupidity: After Ethan "lands in the future", his spacesuit catches fire. He removes his glass head cover (so he can enjoy the smoke in his face?). Instead of following the well-known "drop and roll" technique for smothering/ putting out the flames, Ethan stood there and patted the flames on his wrists and legs with his gloved hands, but the flames were spreading. His next idea was to remove the spacesuit. After a short struggle getting it off, Ethan was no longer "on fire" - so now he dropped and rolled. (00:29:39)
Stupidity: Two things: 1. I find it inconceivable that there is only one Carbon Dioxide Removal Assembly (CDMA) and no spares for a two-year mission. 2. The crew has 20 days to fix an oxygen problem. The commander decides on a 10-day window. 5 days into that window they try to load oxygen from the Kingfisher spacecraft. One is lost into space. Zoe decides to go and fill the other one in the midst of a solar storm that will only last hours. Why take that chance? A few hours wait is still quite possible.
Stupidity: The Analyst wishes to hide the true identity of Neo from anyone inside the Matrix, so his appearance is altered. But in this new Matrix Neo is also named Thomas Anderson, his name from before he was pulled from the Matrix originally, and he is a famous game developer that created a video game series called "The Matrix." It is frankly astounding that anyone actively looking for Thomas Anderson would not immediately see through this ruse and instead would be fooled by balding hair.
Stupidity: The "body armor" General Ford and others wear is very bulky and appears to be quite heavy with all the attachments (e.g, flashlights on shoulders). With the protective suit protruding perhaps 8", it would most likely restrict/slow movement, contrary to what soldiers need. Moreover, the body may be protected, but there's no protection for the face/head, leaving them exposed/vulnerable. Today's products tend to be lighter, thinner, and stronger, so would be expected in the future.