Stupidity: For a brilliant criminal mastermind, Cyrus makes so many idiotic mistakes. (1) He leaves his entire escape plan hidden in the wall for the guards to find later instead of trying to dispose or destroy them (2) He makes the fatal mistake of trusting Santiago completely and never suspecting a double-cross. At the very least, he should have checked all of Lerner airfield just in case the plane was hiding (which it was). (3) He never notices or even questions Billy Bedlam's sudden absence until he sees his body. Odd considering he notice Santiago's absence immediately. And (4) When escaping on the firetruck, he (pointlessly) chooses to ride on the ladder instead of the front seat where he stands out, and Poe and Larkin both spot him. No surprise his whole plan failed.
Stupidity: Ghostface ambushes Sidney and her friend with the two detectives protecting her while in the car. Ghostface busts out of the driver window, and slashes the throat of the driver detective and then assaults his partner, kicking the crap out of him. Ghostface is obviously going with the intent to kill and has a weapon. He just killed one of the detectives and threw the other in the street in front of the car. When Ghostface jumps in the car to take off, the living detective, beaten, jumps up with his gun trained on Ghostface. But rather than do anything smart, he just yells at the killer, the cop killer, to freeze and get out of the running car that he's standing in front of. He just saw the guy kill his own partner and knows he is intending to kill the girls in the back. His gun is pointed at Ghostface who is about to drive over him, but he just yells at him instead of shooting.
Stupidity: Jeff should have just locked Red and his crew in the cellar using the key that Arlene used to open it. Instead he barricades it just so Billy could ultimately get access to it. Had Jeff locked it with the key and then taken the key with him, Billy wouldn't be able to free them. Jeff could have then just called the cops and told them where the kidnappers were contained, and then maybe later Billy could just get arrested.
Stupidity: Central to the plot is the layout of the Mars lander. There are no seats or any restraints of any kind in the lander, which is ridiculous. Spacecraft require safety belts in order to prevent astronauts from being injured during rapid course corrections. Additionally, ordinary rolling desk chairs would not be sent into space, and would certainly not be placed on a landing vehicle.
Stupidity: Anyone with a job in the White House would have to be known to the Secret Service on a daily basis, so the two Secret Service agents that find Cory the janitor should have been aware of his identity without him having to state who he was and that he worked there.
Stupidity: When Alice opens the door for the dumbwaiter, how did she not see the bottom of the elevator was removed when she was looking right at it? She even realised it was missing as she was getting in, but she still let go and fell to the basement.
Stupidity: When White and Exley meet outside the motel and realise they've been set up, White suggests they leave, but Exley says it's too late. It wasn't even close to too late. There were no other people around, they had cars and there was a road right in front of them. Then they decide to go trap themselves inside the motel. It seems like they wanted to be shot.