Stupidity: Billy and Allie saw there were several men in the area also searching for the medallion and the kids even hid from the men minutes before finding the medallion. Instead of quickly sneaking away after they found the medallion, Billy and Allie stayed in the same spot and Billy shouted, "We found it! We found it!" Seconds later, two men came from behind the tree. (00:24:00 - 00:24:21)
Stupidity: For Sarah's murder to work, a lot of coincidences and unpredictable, convenient behaviour from the victim have to happen; she has to Miss the security guard and not hear them, she has to seek shelter of all places right in the costume room full of effigies of the killer, where the killer himself happens to be posing, she has to be completely inefficient at calling help with her cell phone.
Stupidity: The "body armor" General Ford and others wear is very bulky and appears to be quite heavy with all the attachments (e.g, flashlights on shoulders). With the protective suit protruding perhaps 8", it would most likely restrict/slow movement, contrary to what soldiers need. Moreover, the body may be protected, but there's no protection for the face/head, leaving them exposed/vulnerable. Today's products tend to be lighter, thinner, and stronger, so would be expected in the future.
Stupidity: When the Hilts discover they're 20' short of the trees, why wouldn't he "dirty up" his white/light tan pants so the tower lights wouldn't expose him so easily?
Suggested correction: Because he would look scruffy and dirty once he got out. He was the Cooler King and knew his way around after all.
I would suggest in the reality of the escape, light colored clothing would not have been worn so as to blend in to the night and the surrounding environment better. The light slacks were strictly for artistic reasons.
Stupidity: Jake uses several Loops and travels all over the world in order to get back on the boat at the end of the film. This was completely unnecessary as only the final Loop in 1942, which was available to him in 2016, was the one he needed to enter despite the fact that its nature should have prevented him from reaching 1943 anyway.
Stupidity: It was announced on the radio "to stay inside your homes and to only leave in a state of absolute emergency." Then the house shook from an earthquake. May's mom (Gran) called and said, "I'm not sure you should come right now... the roads aren't safe" and "it's not safe to be driving around out there, especially with the kids." May, who told her mom she had the trip planned, finished packing and said, "Kids, we're leaving." Before driving very far, a "monster" was near her car. (00:01:33 - 00:03:47)
Stupidity: After making love, Selina notices Batman's scars. She surely was caught in the moment, but, it's something she really was bound to notice sooner. (00:53:10)
Suggested correction: She notices the scars on his back first, which are the worst of those on his body, this may well be the first time she sees his back.
Stupidity: There is a map of the area on the wall behind Jason as he tells Sam and Ben to "look for anything useful - maps, food, radios, anything." Also, there is a map in the drawer as Sam opens it, but she removes the notice letter "shuttered for budget cuts" and the snowmobile keys. (00:44:43 - 00:45:20)
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 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: 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 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: 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.