What would you call someone who never does anything wrong?

One phrase that comes to my mind to describe someone who never does anything wrong is "goody two shoes." The phrase refers to a person who is obviously, almost flashily well-behaved and virtuous. It comes from a tale called the "History of Little Goody Two-Shoes," a children's story about a young orphan girl who works hard, does everything proper and right, and is eventually rewarded with the love of a wealthy man.
It might be tempting to characterize Mr. Hooper as a goody two shoes because he is a minister and seems to behave so virtuously, until he begins to wear the black veil over his face. Through various clues in the story, we can surmise that the veil symbolizes the secret sin that Mr. Hooper hides from others: the secret sin that each of us hides from everyone else. One theme of the story addresses the fact that each one of us is, no matter how well we hide it, a sinner. Thus, according to "The Minister's Black Veil," no one is truly a goody two shoes because we all have the secret sin symbolized by Mr. Hooper's veil.