
Stupidity: After hearing the question on the radio station to win the Turbo Man doll and a failed attempt at the pay phone to answer it, Howard and Myron end up running two blocks to the station to answer the question. This is really stupid because the prize was going to the first caller with the answer and in the few min it would take to run to the station two blocks away and finally reach the DJ, many calls would have come in and most likely someone would have won already, way before the men arrived there.
Suggested correction: This isn't a stupidity or a mistake. What else did you expect them to do? Plus, the DJ even later asks if they expected him to actually have a Turbo Doll in the studio, and they both said "yes."
Not only that but, Myron had ripped the phone receiver out so Howard couldn't give the answer to the DJ. Howard and Myron running to the radio station was the only other option they had. At that point, it would only be a matter of if they got to the station in time before somebody could call in with the right answer.
It was a very easy question naming santa's reindeer. Although some people may not quite know them all... most people do. Now if it was a relatively hard question, our two guys probably had a better chance. But all good points made here in all these comments.

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: Natasha is in Norway on the run - Norwegian radio mentions her by name, Yelena talks about her being on magazines, she's very recognisable, and yet she goes into a gas station with her sister without changing her appearance in any way, and loudly talks about being an Avenger and killing people, right in front of the gas station attendant who for all she knows would be on the phone to the authorities the second she's out the door.

Stupidity: The coast cities should have an alarm that detects the Kaijuns. If they do, they should work when the beasts are few miles away from the shore in order to give the people time to get to the shelters. Instead of that there are still people on the streets in Japan and on the docks in Los Angeles (in the flashback) while the kaijuns arrive from the sea.

Stupidity: When the crew think that Dorothy is a robot with a bomb planted in her and is capable of exploding, they begin to think that she is about to explode and attempt to dodge it. Rather than hide somewhere or take cover behind an area that may protect them, they just get down on the floor in front of them and cover their heads with their hands. If they thought the explosion was going to be as deadly as the one they saw on the news, this method of taking cover wouldn't be even remotely effective. (00:24:40)

Stupidity: When the Pteradons are loose and flying over the crowds, people run from inside buildings out into the open where the birds are attacking people. (01:22:00)
Suggested correction: A person is smart, people are stupid. A crowd in a panic would do exactly that sort of thing. Like trampling over each other running in panic from a shooting or a fire when not needed. It's the nature of panic in humans as a group to act stupid. It's not a movie mistake. It's actually one of the more realistic parts of the film.
Suggested correction: The dinosaurs were also breaking into/attacking people inside, so they weren't safe no matter what.
True, but one option is certainly safer than the other.

Stupidity: All the mutants on the island need Magneto at the last second to take control of the missiles so they don't land and explode. Why didn't Azazel just teleport everyone off the island?
Suggested correction: Given the situation, there was probably very little time to come up with a plan like this. The missiles were flying towards them extremely quickly, and there would have been nowhere near enough time to band every single person together for Azazel to teleport them all out of there in just a few seconds.
There was plenty of time. He could have taken 5 at a time down the Beach 3 miles and came back for the rest. Earlier in the movie he was moving so fast men were falling from the sky at nearly the same time and he was teleporting them one at a time.

Stupidity: Any fighter pilot should know better than to attempt a low flying attack so close to a hill, let alone into a tunnel. How could he not know that it was there? How'd this moron even get his pilot's license?

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: 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: 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: At the end of the plane chase Bond fails to finish off Hinx. Regardless whether he thinks he's dead or not, with a licence to kill he should have made sure.

Stupidity: Why would Stanley say the shoes fell out of the sky? It happened under a bridge. Any normal person would instantly realise someone threw them off the bridge.
Suggested correction: It's an idiom/expression. When something turns up out of nowhere, we say "it came/fell from the sky." In fact, Mr. Sir says this to Stanley when he finds Stanley with his empty bag of sunflower seeds, "Where did this come from? Did it fall from the sky?" Obviously a sarcastic way of saying, "it didn't get there by itself, someone put it there." So the shoes obviously fell from the bridge and Stanley knows this because Zero refers to the bridge later in the movie.