Honestly I haven't gotten that far into the story for any of my central characters' flaws to seriously affect the core story; In fact I haven't even introduced all of my central characters yet.
But I do have some ideas in mind: There are four members of this, lets say, "action squad" that goes around this fictional world doing Interpol stuff. The first is insecure and prone to doubting himself; the second is similar but hers stem from a different past and treats it differently. The third is lost in the past and doesn't understand current times; the fourth is cocky and arrogant to a point where it's detrimental to himself and others.
I'm seeing it with the question of how those seemingly simple traits can swell in situations that become far more complex than first assumed; that's where their flaws will affect how the story will unfurl:
- The first is in a leader position and is in command of the other three, so how will his lack of self-confidence affect said leadership?
- The fourth has a history of scientific research (and has garnered a stellar reputation for it), so how will he react when his reputation is on the line due to concern over his research being used for negative purposes?
- The second follows orders and protocols to the tee, so how will she react when this steadfast loyalty (due to lack of confidence in her own abilities) could serve to harm rather than protect?
- The third holds an important moral position, so how will she handle that kind of responsibility when the story calls for it?
However, I've been very interested in a second thing, which is the relationships between each character in this "action squad", and how these relationships can build character development and further affect the story as a whole:
- The first and second both suffer insecurities, but the first treats his in an effective way while the second doesn't even recognize her issues. How can they interact with one another regarding this similarity?
- The first and fourth are polar opposites in personality, and they've had a rough past with one another. They're stuck in this "action squad" now, so how will they develop each other's characteristics?
- The second and third are both soldiers who are expected to obey orders, but they both come from vastly different times and viewpoints. How will they complement each other regarding their loyalties?
yada yada yada; there's a lot more than those three, but you get the point.
I think character flaws affecting a story is only half the argument. It's like a feedback loop, where changes in the story affect the characters back, and they start to treat those flaws in a certain way, which leads to character development. I'm pretty sure you get that, seeing how you want your character to introspect on himself and the situation around him. I'm just suggesting that you could take those flaws to the next level; not just have those flaws shape the plot, but also have them cultivate relationships between other characters.
Sorry for the PhD thesis, but I hope it helps expand your story's potential.