"The Minister's Black Veil" largely conveys the idea that people have the potential for both good and evil through the characterization of Mr. Hooper, the minister, himself.
Mr. Hooper is routinely called "good Mr. Hooper" by both the narrator and the members of his congregation. Further, he's always "had the reputation of a good preacher, but not an energetic one: he strove to win his people heavenward by mild, persuasive influences, rather than to drive them thither by the thunders of the Word." He is no fire-and-brimstone preacher who tries to scare his parishioners into right behavior with threats of eternal hellfire if they do not repent and change. Instead of threats, Mr. Hooper prefers gentle encouragement. To him, his job is not to scare his congregation but to urge them into right behavior with his gentleness and care. He builds them up rather than tearing them down. Mr. Hooper has only ever been known as kind and good by his flock.
However, it may be his reputation for goodness that actually causes Mr. Hooper to feel that wearing the black veil is necessary. In a conversation with his fiancee, Elizabeth, Mr. Hooper reveals the veil's meaning (in a very veiled way - pun intended!). He says,
"If I hide my face for sorrow, there is cause enough, [...] and if I cover it for secret sin, what mortal might not do the same?"
Elizabeth sits silent for a few minutes, "But, in an instant [...], a new feeling took the place of sorrow: her eyes were fixed insensibly on the black veil, when, like a sudden twilight in the air, its terrors fell around her." Suddenly, the veil's meaning becomes clear to her and she leaves him forever. What she has come to understand is that the veil is a literal, material symbol of the unseen veil that Mr. Hooper believes each of us wears in life. We each present to the world the aspect of goodness -- as he has done -- and we hide our secret sins from one another, essentially lying about our true natures, and this "veil" of lies separates each of us from our fellows. We can never truly be known by another, and we can never truly know another because we insist on hiding the very thing that actually unites us all: the fact that we are, each of us, sinners.
Therefore, Mr. Hooper has shown his own capacity for goodness and for sinfulness (or evil, if you prefer) through his reputation, what people observe to be true of him, and his decision to don the veil, an attempt to remedy the inaccurate picture painted only by his reputation. Knowing that what he was presenting to the world before he put on the veil -- an image of only purity and goodness -- was a lie, he attempted to rectify it and convey something more true than his reputation alone can ever be (precisely because he hides his secret sins from others, as we all do): that good and evil combine in each of us.