Do you think this story is meant to suggest that the world was fatally flawed, or that is was nearly perfect except for one serious flaw?

I'm not sure these two ideas are mutually exclusive. One serious flaw could very much result in the world's being fatally flawed, especially if that flaw is unlikely to abate or diminish. In this story, most of the people of Omelas are content to accept their happiness at the cost of one child's abject misery. They are, in a word, selfish. Horribly selfish. They find ways to justify the child's continued torture so that they can go on enjoying their idyllic lives—and, let's not beat around the bush: it is terrible torture to sit in one's own excrement, never allowed any real human contact, taken from one's family and home, and fed nearly inedible garbage day after day.
Is there any way that human beings can give over being selfish, learning to place others' needs ahead of our own or, at least, thinking of others as being as deserving of having their basic human needs met? Given the humanitarian crises that go on all over the world even now, and the way many people choose not to act against them, I would say no. Many people would argue that humans are, by nature, selfish and place their own needs ahead of others'. I personally disagree with this idea, but I do think that most people choose to be selfish for a variety of reasons. This selfishness may only be one "serious flaw," but it seems serious enough to amount to a fatal flaw.