
Stupidity: Very soon after Damon is stranded, one of the many satellites around Mars inevitably picks up the fact that he has moved various objects around his site, indicating that he's still alive. Yet it never occurs to him that this would obviously, eventually happen. In which case, his best option would be to simply spell out a message with debris and stay put instead of planning some 50-day journey.

Stupidity: When the policeman comes for the girls, the people run along a straight path, completely straight, without bothering to go over the fence right next to them or run in a different direction.

Stupidity: Kora and Gunnar arrive at the town to find the rebel Bloodaxes via a contact of Gunnar's. They literally see this contact being hauled out of a bar by bounty hunters who work for the Imperium...and then walk straight into the same bar and start openly talking about needing to find the rebels right in front of the bartender and other patrons, who for all they know are all Imperium-aligned.

Stupidity: The whole movie necessarily has to be filled with stupidity (we're talking about a 9 months kid besting 3 adults), but there's one part perhaps not so obvious and that may be related to a mistake about the ransom note. When the bad guys watch the news, it's obvious that their original plan failed, since they cannot retrieve the money at the designed drop zone, the police have been called and they'd need to rethink the whole operation. Yet they make no comment about it and don't seem bothered by that at all.

Stupidity: So if Harley Quinn drove the truck to blow up the plant, wouldn't she have had to drive through all the cop cars at the bar murder scene? We know it was the same street because the cop gives the necklace to the detective. (00:10:58)

Stupidity: When the duke approaches the wall at the end, Snake dives on him and briefly knocks him out. Snake could have easily grabbed his gun back and left the duke unarmed (or even just killed the duke there and then), but just gets up and runs, leaving it with him.

Stupidity: Unless Snow has solid proof like pictures or video why should Katniss believe her main enemy's word that it was Alma Coin, not him, who killed those kids?
Suggested correction: This is a question and not a stupidity. Katniss didn't just accept Snow at his word. Earlier Gale had mentioned an attack strategy to inflict maximum casualties on medics that matched the attack on the Capitol. Then Gale could not deny his part in Prim's death. All the evidence pointed to Coin being responsible as Snow suggested.
I appreciate responses here because it means you're reading stuff and that makes my day.

Stupidity: When Jonathan is chasing the truck to try and save Sarah, he could have removed his heavy backpack and run faster...but instead just leaves it on. No wonder he wasn't fast enough.

Stupidity: The highly trained commandos who knew everything about the NSA base and penetrated it during a perfectly planned operation through weapons and devices that pierce steel like butter, decided to stand outside the barn (so they knew something valuable was there) and its wooden door. It even has a direct line to the command center.

Stupidity: The bad guy who spies on Bosley is visible from the very beginning of the scene, when Elena is not even inside the cafe yet. The cafe does not have many customers and the bad guy is using a loud vintage typewriter with a big mirror mounted on top (!). The Angels are portrayed as being super smart and their setup is so careful, but somehow they managed to miss something amazingly obvious. Conversely, nobody would have ever paid attention to a laptop or any silent, modern-age device perhaps with a camera or something similar, so the bad guy chose the most blatantly conspicuous accoutrement for his spying job. Try showing up to a cafe punching the keys of a big clunky typewriter and literally everyone will be looking at you. (00:18:25)

Stupidity: For being a ruthless race of conquerors, every Kree in this movie is awfully cautious when pulling the trigger. From the kree soldiers who don't shoot the prisoners who were already set to be "ejected into space" (instead of being shot on the spot) nor the space monster attacking them with tentacles, to Yon-Rogg and Minn-erva who do not shoot Carol when she is about to destroy the engine (Minn-erva especially should have no problems doing that and it's the whole purpose of a sniper). The best bit about the shooting idiocy happens when "Just a girl" starts playing, and Minn-erva with 2 soldiers armed with rifles from an elevated position do not shoot their precision rifles but rather jump down on the same level as Carol for absolutely no reason. Which soldier with a rifle would get closer to the enemy?

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.

Stupidity: Leonardo could use his swords to cut the net when Leonardo, Donatello, and Michelangelo are trapped in a net.
Suggested correction: While trapped in the net, it would have been quite difficult for him to draw his swords from the sheath on his back.
While that is true, him not attempting to reach his swords makes him look like a fool that forgot he has swords.