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.
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Stupidity: Throughout the movie, and especially up on the top of the apartment building before they get rescued at the beginning of the movie, Gerry counts 12 seconds to check if someone has been infected. Just to mention this apartment example, he gets blood on his face and spends more than 12 seconds getting up and to the edge of the roof, plenty of time to become "Zeke." He then counts 12 seconds, as if they would actually matter to his infection.
Stupidity: After Corinne Dufour realises that Drax intends to have his dogs kill her, she inexplicably attempts to flee on foot, running right past the golf cart she arrived in. The golf cart would have given her more speed, range and protection, and would have been a much better choice for fleeing.
Suggested correction: Golf carts are very slow, and are open on all sides: the dobermans would've easily dragged her off it. The biggest stupidity here is that she should've fled to a crowded area with other people instead of the woods. Then again, she was panicking, and not thinking straight.
Stupidity: When the Woolworth Building collapses and the gang runs into the convenience store to take cover from the dust, Marlena was last seen behind Hud and with Lily, Rob, and Jason. Switch to everyone running from the dust cloud, Marlena didn't make it into the store. Upon exiting the store, the gang finds Marlena stumbling from nearer to the Woolworth Building meaning she would have had to run toward the dust cloud, through the screaming crowd which was running away from the building.
Stupidity: Cobb convinces Fischer to enter a dream saying it's Browning's dream. A couple of scenes later he says it's Eames' dream, in front of Fischer, who doesn't know Eames was impersonating Browning. (00:51:35)
Suggested correction: Firstly, the Browning that the team "catches" is not Eames, it is a projection of Fischer's subconscious. Eames was only impersonating Browning in the first level. Secondly, Cobb doesn't say they are going into Browning's dream, he says they should put him under and do to him what the kidnappers were planning to do to Fischer. That is, use Fischer as the subject of the next dream level. Fischer knows that Eames is the dreamer on the third level, he even jokingly asks why Eames couldn't dream of a beach. But he thinks that Eames is part of Mr. Charles' security team. He believes that Browning is to be the subject on the last level when in fact, Fischer is the subject on each level. Because of how effective the Mr. Charles gambit was, Fischer is unaware that the team has been fighting his subconscious all along.
Stupidity: This highly trained squad of soldiers is sent into a known contaminated zone with all manner of chaos going on within in...and the second one of them sees a woman outside his APC he ignores a direct order and pops outside to see how she's doing.
Stupidity: After Ethan "lands in the future", his spacesuit catches fire. He removes his glass head cover (so he can enjoy the smoke in his face?). Instead of following the well-known "drop and roll" technique for smothering/ putting out the flames, Ethan stood there and patted the flames on his wrists and legs with his gloved hands, but the flames were spreading. His next idea was to remove the spacesuit. After a short struggle getting it off, Ethan was no longer "on fire" - so now he dropped and rolled. (00:29:39)
Stupidity: Wouldn't it be common sense to have more than one remote to control Robo-Cain? That way, if he destroyed one (and he did), they could still use one to shut him down from a distance (as long as they can dodge the gunfire).
Stupidity: All of Robbie's circuits have been burned out as a result of Morbius ordering him to kill the Id monster. The crew only has 24 hours to get the ship loaded and a safe distance away from Altair IV before it explodes. But one or more of the crew spends the little time they have fixing Robbie, a very sophisticated piece of technology, who is working the controls at the end of the movie.
Stupidity: Project Pegasus is a billion dollar structure with no security guards besides the couple dudes Fury shows the badge to at the entrance, no video surveillance, and once SHIELD arrives nobody has to even open a locked door anymore.
Suggested correction: First of all, Fury was allowed in as it's a government facility and he works for the government and as a SHIELD agent is allowed access. It's inside a mountain and they passed multiple security guards as they drove in, armed guards. Everything is thumb prints and cameras which was quite elaborate for that time. To say they lack in security is quite an understatement. SHIELD has quite some authority and can easily take control in the Pegasus project facility.
You are right about the main entrance being truly secure both for guards and strategic position. The problem is that they are free to just roam the facility for an hour, blast through doors, not a soul in sight, no evidence of camera monitoring the inside of the structure, and once the gag of the pad is finished, no door requires it. Actually, funnily enough you can see a guard of the place opening the elevator for Fury and the supervisor, as if the thumprint scan was needed to even get into the elevator itself, but Keller then just walks into the archive just fine (from a different door than the one Vers blasted). There are keypads to exit places (for instance the hangar, when the agents in pursuit break through the door you can see a keypad on the wall) but only when it's convenient (Vers and Fury walked through that same door with no problem, not to mention the fact that the whole stairs seem to have none, which is funny for a place that has keypads both sides of doors).
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: It's mostly a fun absurdity, but it is somewhat contradictory to showcase the Ghostbusters being featured as the cover story of every major publication and news outlet, and yet to get help not only they put an ad on the newspaper, but a single person applies for the job (which is all it took for them to accept).
Stupidity: When Michael is heading to the hospital and he just learns that the Cloverfield Station is gone, the whole scene of him driving is super unreal. It looks like he's not even driving, like it's a self-driving car or something because the steering wheel doesn't move at all while he's driving, and he isn't looking at the road (staring into space). The whole scene just doesn't feel realistic. (00:43:48 - 00:44:30)
Stupidity: The Analyst wishes to hide the true identity of Neo from anyone inside the Matrix, so his appearance is altered. But in this new Matrix Neo is also named Thomas Anderson, his name from before he was pulled from the Matrix originally, and he is a famous game developer that created a video game series called "The Matrix." It is frankly astounding that anyone actively looking for Thomas Anderson would not immediately see through this ruse and instead would be fooled by balding hair.