If you're a writer, especially one who researches their subject and finds something that is absolutely unbelievable, but true - resist! Resist that urge to slip it in. It's unbelievable and that's the bit that matters.
Here's some examples of how it can go so wrong...
I love what used to be called dine-novels, those trashy pulps full of action and cliché. One particular series I devoured as a teenager was set in a post nuclear war world with hardy men and women fighting for freedom and democracy. In one book, the hero's sidekick gets shot in the head and the bullet bounced off. That was the end of it for me. Now I know of dozens of cases where bullets have bounced off peoples' heads. Bullets at extreme range, with little energy left, will do hardly any damage. If the glancing angle is just right it will bounce off when it is full of lethal energy. These things have happened. In this story the shot was at near point-blank range. It broke the story. The author even tried to justify it in the text, which made it even worse. By the way, if you've ever wondered about the definition of point-blank range see below.
Another incredible happening is falling from great heights and surviving. Air stewardess, Vesna Vulović, survived falling 33,000 feet (10,000m) when her plane exploded. There have also been tales from World War II about pilots surviving falls into forests and snow banks from around 20,000 feet (approx 6100m). Window cleaners working on skyscrapers have used up all their luck in one fateful, but survivable fall. I've put a link below to ten amazing and true stories of survival.
If you put that in your story be very careful. I read a massive international best seller, I won't name names because that's like slipping in spoilers, but the hero leaps from a helicopter at 20,000 feet and is saved by a bit of canvas and falling into a river. I'm not a fictional hero so don't have a grip of iron (imagine the forces trying to rip that fall-slowing cloth from your hands) or have the mental constitution that would allow me to function after a trauma like that, but he carried on. That particular work had been wavering on the edge of believability all the way through and that just did it for me. I'll never read his work again.
Writers do get it right by avoiding this, but doesn't stop you using it. In Bernard Cornwall's Sharpe series there are various episodes where people are killed by having nails hammered into their heads. If you do a quick search of the Internet you'll find many tales of people surviving this kind of event. Cornwall is spot on with this kind of violence being fatal, but we know it's not always. Perhaps a modern day revenge thriller could start with a torture sequence with the villain 'killing' the protagonist with a final nail, but of course they fail. Already, in one sentence it sounds unbelievable. I just keep think of him setting off security scanners.
Very recently I heard of one Harrison Oknene, a Nigerian Cook aboard a tug that sank in around 100ft of water (approx 30m). He survived trapped in an air pocket for three days and was rescued by the very surprised divers looking for bodies. If you put that in a story, would it bounce the reader? I don't know, but you'd have to be careful about how your hero escaped. If Mr Oknene had managed to find his way out of the upside down ship, in pitch black freezing water, and risen to the surface (note, he may have been at his negative buoyancy depth) he would have contracted the bends (nitrogen poisoning) and died. He had been down so long that he had to undergo hours of decompression like the divers who saved him.
Having said all that, if you absolutely have to, limit yourself to one unbelievable thing in your story. Keep it to one no matter the temptation. A bit like coincidence, just keep it to one. One unbelievable coincidence is stretching it a bit, two and you kill the story. Like Mark Tawin said:
'Truth is stranger than fiction, but it is because Fiction is obliged to stick to possibilities. Truth isn't.'
Where does this ramble come from? Well, I watched a TV show where they were making fun of James Bond creator Ian Flemming quoting a martial art technique that they couldn't believe was real. Funny thing is, I have seen it demonstrated. If I told you what it was, you wouldn't believe it either.
Definition of Point-Blank Range
Point-Blank range is where the distance travelled by a bullet is so short for its size and velocity that it follows a flat path. Any further and the bullet will start to drop as it is pulled toward the ground by the Earth's gravity. Beyond Point-Blank range a projectile will follow the classic parabolic curve of all projectiles.
Weird fact: if you drop a bullet and fire one horizontally at the same time they'll both hit the ground at the same time too.
Negative Buoyancy Zone
There is a depth at which the human body is no longer buoyant. It is dependant on body size, type and lung capacity, but at that point you need to work very hard against your own weight to reach the surface before your air runs out. It is often what kills free divers when they can't get to the surface on the oxygen left in their bodies.