I have a rabbit problem. Not in the garden, in my books. And if your characters are as capable as Jack Reacher or as smart as Sherlock Holmes or as beautiful as a fashion model... or in anyway presenting themselves to you as nearly super-human, then you have a rabbit problem too.
Legendary Warner Brothers animator Chuck Jones also had a rabbit problem. He was possessed of a set of characters with the ability to bend reality to their whim in order to triumph over what seemed to be overwhelming odds. And at the head of the pack was a rabbit named Bugs.
"Golden Rule. Bugs must always be provoked. In every film, someone must have designs on his person: gastronomic, as a trophy, as a good-luck piece (rabbit's foot, which makes as much sense as a rabbit carrying a human foot on a key chain), as an unwilling participant in a scientific experiment [...] Without such threats, bugs is far too capable a rabbit to evoke the necessary sympathy."
-Chuck Jones "Chuck Amuck"
Take the above quote and insert "Sherlock Holmes" or "Jack Reacher" or "Calvin" from Calvin & Hobbes in the place of Bugs and you'll see the problem that Conan Doyle, Lee Child and Bill Watterson faced every time they sat down to write.
If you can take your lead character(s) and insert their name and gender into the above quote, then you're in the Radio Flyer wagon with Arthur, Lee, Chuck and me, staring around at the sea of rabbits. Welcome aboard! The blonde kid with the tiger is in charge, so don't smart off.
If a drama is derived from ordinary people in extraordinary situations, is it worthwhile to examine the extraordinary person in the extraordinary situation? Of course it is. It's just a matter of how you go about it.
The first thing to remember is Chuck's admonition that the supremely-capable character acting unprovoked will elicit very little sympathy from the audience. The corollary to this is that watching someone who is smarter than the subject matter waltz through the story is boring to boot. The Rabbit has to meet a challenge worthy of his efforts and attention or I'm not going to read your story and most of the editors I've met won't either.
Incidentally, if your character is so talented and capable in every realm and situation, I humbly submit that you need to rethink the decisions that led to your writing a novel about Superman. (Unless you really are writing a novel about Superman, in which case good luck and Godspeed because I'm as big a geek as as the next guy.)
There's a trap that catches just about every writer early in their writing career: It's insanely easy to create a fantasy alter ego that is everything we ever dreamt of being. And because as a breed, writers tend toward the bespectacled introvert more than the opposite. (There's a fine line between being stereotypical and merely archetypal.) With godlike powers, we can make manikins of words that are smarter, faster and better than any human being could ever hope to be.
There are degrees of extraordinariness and I should take a moment to poke some holes in...
Contrary to what detective novelists and television have taught us, a genius IQ does not automatically come with a detective's badge, Oriental lineage doesn't come with a black belt in the local martial art and very few CIA employees ever get issued a Glock and a license to kill. Those things are all cliche's. That's not to say that there aren't any genius PI's, Japanese kids trained in Ninjitsu or CIA hitmen in the world, just that there's a fine line between stereotype and archetype and in a fictional setting the scales are too often tipped toward the wrong side of that equation. (mixed metaphor alert!)
The cliche has a place in writing and life and we should treat them in the manner that they so richly deserve: subversion. Playing against audience expectations is part of the fun of writing the extraordinary character.
Drag your Rabbits out of their element. Give them a reason to get involved and then challenge them by forcing them to act in a realm beyond their expertise. Play them against themselves and keep doing it or you're going to end up running afoul of Chuck's Golden Rule. At which point, you might as well lobotomize your rabbit and let the hunter catch him.