I knew that a lot of writers considered heroes passe', but I had a different pov. I'm married to a hero with more virtues than you can shake a stick at. So when I arrived, I knew pretty well how I'd start out. As expected, the other panelists scoffed a bit at 'perfect' heroes and how unbelievable they are and boring, etc. Then I brought up how real heroes feel real pain, fail, struggle, and how their morality and ideals cost them (sometimes dearly.) The tone of the panel changed a bit, especially since I had Alma Alexander on my side (to an extent) because she knows my DH and realized what I was talking about. We began defining which led to a discussion of the difference between a good guy and an untouchable perfect darling, and I began learning, which is one of the fun parts of being a panelist. Panels can be about the brainstorming, and this is definitely one of those.
There's a difference between a 'perfect' hero and a guy who does the right things, fights hard, loves hard, and doesn't have a dark past or skeletons in his closet. The darling hero defeats every villain, crashes through every obstacle, and does it without breaking a sweat or a hair out of place. Often the obstacles s/he faces aren't on his (or her) level; they're no match for the might of the darling hero. *That's* what's boring.
Now, some authors deal with an otherwise unstoppable hero by developing an equal or even more powerful villain or insurmountable problem. This is the superhero route, though they aren't always called superhero stories. In a way, Gandalf vs. Saruman is a superhero/supervillain story. Gandalf can otherwise plow through just about any obstacle. Tolkien had to put a balrog, a fellow wizard, and the Witch King in Gandalf's way before Gandalf broke a sweat. It's different than a darling hero, and it can be a fascinating read. I loved The Dark Knight movie. That worked for me.
Personally, I prefer a morally principled hero who will not cross certain lines, who won't cheat on his spouse, and who won't call in sick to work unless he's actually sick. Boring? Well, when it seems like he's the only one who cares, the only one willing to put his ass on the line to speak out against bureaucratic bs, and the only one who doesn't want to go to the strip club because the drinks are overpriced and he prefers to watch his wife dance, thank you, it can get pretty lonely. In fact, it can get dangerous. Remember the 'okay, on three, everyone charge' type stuff going into a fight? What if your character is the only one who goes on three?
Being good, even great, even the best in combat, or science, or whatever doesn't always save the day. In the real world there are insurmountable problems. Try kicking cancer's ass sometime. How about stopping a line of tanks from plowing into a village by yourself? How about dealing with bad intelligence, or someone outright lying to you about something being one way when it's another? Real heroes fail, and they get hurt, often badly, not just by the thing they're fighting but the consequences of their failure, and also the consequences of success. Sometimes, no matter what you do, there are widows and orphans, and a real hero feels that pain.
Everyone who looks at a too-good-to-be heroine might think no one is that smart, that beautiful, that accomplished. Having a beautiful, smart and physically powerful character can absolutely be annoying in fiction, but only if that character is protected, only if that character doesn't suffer from the sense that she's resented, or always the one asked to do one more thing, the one everyone borrows money from. It can not only be lonely, but frustrating. If the heroine walks on stage and everyone gazes at her with worship, lust and awe, the reader is going to roll their eyes. But think about what really happens, not on those 'grand entrances' but day to day. Sleezebags at the bar trying to pick her up with cheesy lines and offers to buy a drink. The boss that keeps coming up with reasons not to promote her. Seen through her own eyes, she may not consider herself beautiful at all. She may wake up in the morning, stare at the mirror and wonder how she can face another day on the battlefield when what she really wants to do is try to negotiate a surrender before every blessed soul in her army is killed over a land grab.
Writing about teams of these people can be fun as well. Being the go-to team can lead to more than their share of adventure, but believe me, not only can it get tiring, but they can suffer from bad press, back-stabbing from all quarters, undermining, and a desire to take a long vacation but feel like they can't or the world will fall apart without them. Think rock stars have it tough with the lack of privacy, and the hero worship? Try fame, unrealistic expectations and worship on when lives are at stake. Top that with their bosses micromanaging them, telling them 'how' to do something, when they all know that will only get them all killed. And if they succeed their way, they're in trouble, again, as always, and come out looking like the bad guys.
The short of it is: provide conflict, make it hurt, have failures, and use that goodness against the hero. Force your hero to make hard choices, and give him that same sense of isolation that our real world heroes--the dedicated cops, caring firemen, tireless doctors, etc.--often face as they stand alone in a sea of apathy, bureaucracy, greed, selfishness, envy and Monday morning quarterbacking. (That last one is especially frustrating.) Just don't forget to give them an occasional bright spot, like the gratitude of a child, the help of a good samaritan in a time of need, or a moment of peace under a starlit sky, or they'll break like so many of our real heroes break and end up alcoholics, hermits or suicides. Somehow I doubt the readers will complain that your hero is too perfect if you write it like that.
I'll leave you with Cyrano de Bergerac (paraphrased):
Now, who are these--a thousand thronged about me? I know you well--you are all ancient foes; Falsehood! Compromise! Cowardice! Shall I make terms? No, never! There is Folly too! I knew that in the end you'd lay me low. No matter. Let me fight! and fight! and fight! You snatch them all away--laurel and rose! Snatch on! One thing is left in spite of you, Which I take with me: and this very night, when I shall cross the threshold of God's house, and enter, bowing low, this I shall take, despite you, without wrinkle, without spot--and that is--my stainless soldier's crest. [Also has been translated brilliantly to 'my panache' by Anthony Burgess] (translation by Howard Thayer Kingsbury)
Educational side note--panache originally described a white plume or sash carried by nobles, and the pride with which they wore it turned it into a symbol of the qualities we now call panache.