Well, I have to say that there are many perceptions on an event.
Look at Vash the Stampede. Saving the world for him is mechanically very easy. At least in the anime, it seems clear that he could easily defeat and kill Knives and that simple act would save the world. However, he's not just trying to save the world, he's trying to save Knives and that is much more difficult to achieve.
You might have a story where a character has won the treasure, defeated the villain and protected their friends and loved ones.
Something where those outside the character's perspective view everything as an uproarious success, but the Hero still failed in their goals.
Itachi Uchiha likewise had a long, complex plot to redeem his clan and set up his younger brother as a hero as well as killing Madara Uchiha and preventing him from threatening the world any longer. His plot even required him to be a villain and die at his brother's hands. However, he has ultimately failed, (unless that crow in Naruto is another step).
And people do like to read about or watch the unstoppable force.
That's why Columbo was so popular for so long. You knew that Columbo would catch the killer every time, the only question was how he would do it.
As to handicaps and awesomeness, it is all in how they are applied.
Lucretia from my Bystander books can see electrical currents and temperature shifts, even through some walls. Her vision is so acute, that she could recognize people just on their electrical or heat patterns alone and I eventually plan to have her comment that racy pictures only produce a half-hearted reaction from her, because they don't have everything she usually notes in watching people.
However, these two senses are one of Lucretia's most often cursed abilities. Because of her ability to see electrical currents, computers, televisions and most of the movie theaters in her setting (year 2035) tend to be nothing to her except a jumble of electrical signals that completely obscure anything else on it. She even has to have a braille translator for when she's working on the computer at the library she works. Which brings the matter to the temperature vision. Unless the temperature is at a steady rate and her brain starts editing out the extra information, the heat vision washes over her normal vision in a thick overlay which makes reading more or less impossible.
Someone misdiagnosed her with dyslexia and she goes with that even though she's vaguely aware that it's not true.
This is a problem for Lu because reading is actually her favorite activity (yes, she's that desperate for an escape) and she is occasionally described doing something like reading a history of OPEC or the Magna Carta.
By the same token, despite being incredibly stronger, faster and tougher than most of the other characters, she's practically worthless in a fight compared to the humans she commonly hangs out with. All because she lacks any shred of combat training. The leader of the merc team her parole officer hired even goes so far as to point this out in Making a Point (http://thryth.webs.com/bystander.htm). It doesn't help that her official files are free to the public and make clear to the well-trained exactly what her weak points are (joint locks, palm strikes, other vibratory attacks due to the fact that her resilience is because her skin hardens in anticipation of an attack...heat also hurts her more than other things might....). Of course, "weak point" for a superhero translates to "something that they are less invulnerable to", but still.
Lu's strongest points are that she's a cunning little street rat who would probably be rated as beyond a master in terms of picking pockets or locks, and very competent at the short-con and reading people.
any sort of story can make a good one:
Superman, Hamlet, Spiderman, Vash the Stamped, Harry Dresden
It doesn't matter whether your character is always successful or always fails. What matters is that you entertain the audience.
I have been talking about some specifics to writing on my blog. (http://thryth.webs.com/apps/blog/)
I have a lot of ideas in my head for lots of different characters, but just taking my current story that I'm actually writing on paper. My character is far more powerful than he knows, and continues to get more powerful as the series goes on, but the very source of his power is his weakness as well. Or... rather i think with my character it's the other way around... his weakness is the source of all his power. but anyway.
Umm... some good examples of this would be from the dresden files where the angelic power he gets from slaying the coin demon is freakin' powerful but eats at his soul to use it
cast demonic magic, but each time it soils her aura making it blacker and blacker, causing the outside world to view her as a black witch, despite the fact that she's never used magic to harm anyone