Kyoshi's extreme longevity (The Last Airbender): In episode 4 of ATLA, it's mentioned that Avatar Kyoshi had been born 400 years ago, but when you do the math you realize the writers only went with a big number without thinking too much about it. Aang was 112 due to having been frozen in ice, and Roku lived for 70 years. That meant that Kyoshi had to have lived for over 200 years.
Rather than retconning this, the novel The Rise of Kyoshi explained that she had learned a technique to achieve immortality from a man called Lao Ge, who was over 4000 years old himself. They even worked this into Kyoshi's ruthless reputation, as the longer she lived, the more expendable a single human life looked to her, meaning she was more willing to sacrifice people for the greater good. She also lived long enough that she started to see the long term negative effects of her own actions as Avatar earlier in life. While it is unknown how she died, most fans believe that she eventually realized living so long was interfering with her duty as the Avatar so she decided to voluntarely stop using the technique and pass away at 230 years old.
Rick's survival (The Walking Dead): At the beginning of the story, Rick wakes up after being in a coma for a bit over a month to find out that the world had been taken over by zombies. This is a cool premise, until you realize that a person in a coma would probably have died in this situation with nobody to take care of them.
Well, in the web miniseries The Oath, it's revealed that a doctor called Gale Macones, who worked at the hospital where Rick was, stayed behind to take care of her patients. She is gone by the time Rick wakes up, but it was her care that kept him alive.
The Death Star's huge weakness (Star Wars): Star Wars has a lot of these, but this one is probably the most well known. In A New Hope, the rebels get the Death Star plans and realize it has a huge weakness in the form of a small thermal vent that led directly to the main reactor. Later, Luke uses his X-Wing to shoot through this vent, destroying the whole space station. While this is a cool scene, one is left to wonder why the Empire would design their ultimate weapon with such a big weakness that allowed any pilot with good aim to destroy the entire thing.
In Rogue One, we find out that Galen Erso, the main engineer behind the Death Star's reactor, had been tricked into thinking he was working on a project to provide limitless energy to the citizens of the Empire. When he realized it was to power a weapon, he tried to escape but was forced to complete the project. He then decided to sneak a weakness into the design with the hope that the rebellion would be able to use it to destroy it.