Stupidity: Mr, Freeze and Poison Ivy join together and plan to cover Gotham in freezing temperatures and plants, with none of them ever considering in the slightest that plants don't survive freezing temperatures, despite both of them being scientists.
Suggested correction: Poison Ivy made super-plants that could survive the new ice age they were going to create. As for the fate of normal plants, though this is only really clarified in the novelization (and original script), Poison Ivy's god complex has (pun intended) grown to where she no longer cares about individual or existing plants, just playing out her fantasies of being "Mother Nature."
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: 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: The first time they see the bad guy in the Land Rover, Morgan has him in his sights but can't shoot, as he doesn't want to kill him. Clearly, the obvious thing to do is to shoot the car tires, but he doesn't and lets him drive off.
Suggested correction: Shooting out car tires is not an actual effective strategy to get a vehicle to stop. A 9mm bullet simply doesn't cause enough damage to a tire to get it to go flat immediately. It causes similar damage as running over a nail. It is a movie cliche, similar to using a gun to shoot out a lock or a rope, it just doesn't happen in real life.
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.
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.