Are the prophets of God fallible?

In summary I believe this "Question: How are Church members protected against error by leaders?" I particularly like this quote:

"Even with the best of intentions, [Church government] does not always work the way it should. Human nature may express itself on occasion, but not to the permanent injury of the work." (Elder Boyd K. Packer, “I Say unto You, Be One”, BYU Devotional, 12 Feb 1991)

See also, "Are prophets infallible? Statements by Church leaders"

In stating that prophets are fallible, it is important that I also see myself as fallible. I "see through a glass darkly" (1 Cor 13:12) I see the Quorum of the Twelve and the First Presidency as watchmen on a tower who have the commission to protect me. Who have the right and ability to see things that I cannot see and can warn me of things to come that I am not aware of.

I see our church as in the period described by Zenos in his allegory of the olive vineyard.

Graft in the branches; begin at the last that they may be first, and that the first may be last, and dig about the trees, both old and young, the first and the last; and the last and the first, that all may be nourished once again for the last time.  

Wherefore, dig about them, and prune them, and dung them once more, for the last time, for the end draweth nigh. And if it be so that these last grafts shall grow, and bring forth the natural fruit, then shall ye prepare the way for them, that they may grow. 

And as they begin to grow ye shall clear away the branches which bring forth bitter fruit, according to the strength of the good and the size thereof; and ye shall not clear away the bad thereof all at once, lest the roots thereof should be too strong for the graft, and the graft thereof shall perish, and I lose the trees of my vineyard. (Jacob 5:64-66)

The 15 prophets, seers and revelators are following this direction. They are clearing away the branches that produce the most bitter fruit. That includes the results of the culture that we live in and our ancestors. I believe that "If we faithfully proclaim the gospel, we then receive the promise that we will be cleansed from the blood and sins of this generation." (Peter B. Rawlins, "Endowed with Power," Religious Educator 13, no. 1 (2012): 125–139.) I think that the "blood and sins of this generation" includes the bias, misconceptions and incorrect traditions that we have inherited.

I love how President Dieter F. Uchtdorf said it.

We simply don’t know all things—we can’t see everything. What may seem contradictory now may be perfectly understandable as we search for and receive more trustworthy information. Because we see through a glass darkly, we have to trust the Lord, who sees all things clearly. ("What Is Truth?", Dieter F. Uchtdorf, CES Devotional Jan 2013)

If we stay on the old ship Zion, we will be guided safely to receive more light, "brighter and brighter until the perfect day" (D&C 50:24-25). All of the scales will fall off our eyes. We will distinguish all the truth from the error.