The problem with flaws is that you can't just throw them in there to avoid allowing your character to be a Mary-Sue. (Which, no offense, is what the author of Twilight appeared to be doing to a T. I haven't read Twilight and I'm pretty sure I won't ever read it, so I can't say whether this "Bella" person is a Mary-Sue.)
You can't just say, "Oh, she's a little ditzy," and call her a good character. Mary-Sues DO have flaws...but not important ones. Not REALISTIC flaws. That's the rub. If you feel like your character is a Mary-Sue, then it's far better to scrap him/her completely than it is to just throw in some flaws, especially if they have little/nothing to do with the plot. Also remember that realistic characters have multiple flaws...but they don't need to be dwelled on.
I think that's really the problem with characters today--they're too influential. These are called stories because that's the point. Telling a story, not describing this character for six pages. The author spends too much time describing the character's appearance, personality, past.
If you say that your character Tim is a middle-aged banker, I can already get a picture of him in my mind. Unless there's something that you have to say that IS IMPORTANT TO THE STORY (such as he's got a limp which will later make it very difficult to run away from a rabid coyote...) then don't bother. I already understand who Tim is, and I don't need to know anymore, and what's more, if you do the character right then I won't even remember what color hair he has or what color his eyes are or how tan he is. Think back to the last published excellent book you read, and try and remember the character's physical attributes and the plotline; chances are, if the story was written well, you won't remember what color the MC's shirt was, or if you do, you won't remember as well as you do the plot, because that kind of thing should always take second place to the actual story's plot.
Then there's the actual nature of "flaws" themselves. What you consider a flaw, others may not. Some may find that flaw endearing or attractive. The fact that Tim has a limp doesn't necessarily register as a flaw to everyone--to some it's just a medical condition he has. Also, flaws come in a variety of extremity. That Bella is clutsy isn't a mega flaw, unless it REALLY has something to do with the plot. (And I don't mean that she was fated to be clutsy, or something stupid like that.) That Hamlet was too indecisive and therefore, by inaction, caused the death of several people he cared for was a major flaw, even though we may not consider indecisiveness that much of a flaw. Basically, it all comes down to a matter of perspective, and the way that flaw works (or doesn't) in the context of the story.