Do prophets make mistakes?

Yes — plainly, and the Restoration has said so about itself from its first printed page. The Book of Mormon opens by allowing that "if there are faults they are the mistakes of men." The Articles of Faith affirm the Bible as the word of God "as far as it is translated correctly" — declining, in the same breath, to claim scripture is errorless. And in the revelation the Lord placed at the front of the Doctrine and Covenants, he says he speaks to his servants "in their weakness, after the manner of their language." The Church's own canon has said this about how God works through people since before the Church was even organized.

Underneath the question is usually a worry: if a prophet can be wrong, how can I trust any of it? That worry assumes that what holds the Church together is the errorlessness of its leaders — so that one demonstrated mistake would pull the whole thing down. And that assumption, it turns out, was never true. What binds this people is a covenant: baptism, the sacrament table, the temple, a priesthood order, a life lived together. Prophets administer that covenant; they were never required to be flawless to administer it faithfully. The Church asks you to sustain a prophet. It has never asked you to believe he cannot err. No baptismal interview or temple recommend question has ever asked it.

What about the promise that the prophet "will never lead the Church astray"? Read it carefully and it is a promise about the covenantal essentials — the gospel of Christ, the ordinances, the covenant path itself. It has never been a guarantee about every sentence spoken from every pulpit across two centuries. Latter-day Saints are not asked to choose between "prophets speak for God" and "prophets are men of their time," because the tradition's own account of revelation holds both: study, judgment, and confirmation, received line upon line. Real light arrives through real people.

The hard case

This answer would be too easy if it skipped the hardest example. For more than a century, Black Latter-day Saints were denied priesthood ordination and temple blessings, and leaders defended that restriction in explicitly doctrinal terms. In 1978 the restriction was lifted by revelation, and the Church has since disavowed the theories once taught to explain it. There is no honest way to file that under "it was never really doctrine" — and the Restoration does not need that move. Its canon keeps the account of Paul correcting Peter face-to-face over a boundary question, and kept it in scripture rather than tidying it away. What the record shows is that teaching, practice, and eternal truth can come apart badly enough to require repair. Repair came, by revelation, and through the labor of Saints who prayed, petitioned, gathered, and stayed.

You can take present prophetic direction with full seriousness (sustaining the prophet is a covenant commitment, examined at baptism and at the temple) without pretending every teaching in Church history carries a guarantee about eternity. Fallible prophets, reliable covenant. That is the structure of a church with an open canon and a living God.