Stupidity: When the Keymaker is closing the door to the room that leads to the Source, he stands in the doorway resulting in the multiple Agent Smiths gunning him down. He could have easily closed the door without standing in the doorway and consequently would have lived.
Suggested correction: Who says the door was bullet proof and the Keymaker couldn't have been shot through the door?
The point of the stupidity is that he shouldn't have been in the doorway at all, even if the door wasn't bulletproof, there was no need for him to even stand behind the closed door. He could have pushed the door closed from the side.
It seems to be a heavy door, he simply couldn't close it with just his arm, thus he had to move his body forwards in order to close it. In that brief moment he got shot before the door closed. He could have for example kicked the door shut but he simply didn't think of that at that moment, also not knowing the Smiths were about to fire a volley of bullets at them.
Stupidity: The prison where Magneto is held should have had a contingency plan just in case of escape, like machine guns outside the cell, or tranquilizer darts, or gas.
Suggested correction: What good would machine guns and tranquilizer darts be against a man who can literally control and manipulate metal? As for gas, the area outside the cell is so large that any gas would quickly dissipate before it could be effective.
Stupidity: If the doctor was able to choose the people to go on the helicopter, why didn't she make up a reason to put the president's son on the helicopter for his safety? She could have said he was sick. (01:14:40)
Suggested correction: He is shown to be a caring person. There is no way he would take the place of a sick woman or child just to save his own neck.
That correction is illogical though. By not getting on the helicopter he puts everyone else at way more risk. It would have made getting the rest of the people left behind out of danger much easier as they wouldn't have been hunted down by the people who were chasing the president's son. By not getting on that helicopter he could have gotten everyone killed.
Stupidity: When Governor Swann is trying to encourage his daughter while she's locked within the ship's chambers trying to escape, she climbs down to a boat. Nobody in the Navy would have left a boat there, neither would Jack (and why would he, especially without anyone noticing?). The boat just mysteriously appears to help her escape.