What's a hero?
Two of the definitions given by Webster's New World Dictionary, Third College Edition (which I cite simply because it's at hand) are as follows: "any person, esp. a man, admired for courage, nobility, or exploits, esp. in war," and "any person, esp. a man, admired for qualities and or achievements and regarded as an ideal or model." I think most of us would go along with those definitions.
A third definition says that the hero is the main character of a story, and I think most of us who write would tend to agree. But at the same time, as much as we want to write about courageous, noble, and admirable characters, we have to make sure that the heroes we write about aren't perfect.
The fact is, readers don't want to read about people who are perfect. Readers don't mind reading about people who are incredibly competent, such as many of Robert A. Heinlein's protagonists, but if a character is already perfect inside and out, what kind of challenges will that character have to face? There's no possible challenge that will make the reader wonder if the character will make it through. There's also no possible growth for such a perfect, unflawed character.
Not that he's ever been a completely unflawed hero, but Superman represents the need for flaws quite well. The Superman that the character developed into in the 1970s was so powerful that he routinely flew through the heart of the sun to clean off his costume. It became rather clear to the writers that such a hero could foil the average bank robber too easily to make a good story. So the villains in turn had to become more powerful, until the story lines were often ludicrous to the extreme.
The most interesting heros are the ones who have to face their own flaws in order to achieve their goals.