Based on The Scarlet Letter, do we assume that we should be without flaw or sin? Should we never show that we have made a mistake?

In the final chapter of the novel, "Conclusion," the narrator says that "in the view of Infinite Purity, we are sinners all alike."  Therefore, despite the fact that some people try to live without sin—and some others pretend to do so—as human beings, we are fundamentally flawed and incapable of perfection.  If we were perfect, we would be gods.  The narrator claims that we are all sinners, every one of us, and so we cannot ever be totally without sin or flaw in the eyes of God.
Further, the narrator says,

Among the many morals which press upon us from the poor minister's miserable experience, we put only this into a sentence: "Be true!  Be true!  Be true!  Show freely to the world, if not your worst, yet some trait whereby the worst may be inferred!"

In other words, more important than being sinless—which the narrator has already identified as an impossibility—the narrator claims that we should be honest about our sinfulness.  If we are all, at least, honest about our sinful natures (if not our specific sins), then perhaps we will be less likely to judge one another (as the Puritans in the story do) and the guilt we feel for our sins will not be allowed to eat away at us (as Dimmesdale's guilt done to him).