The Church of Jesus Christ of Latter-day Saints is led by Jesus Christ via a prophet and 12 Apostles just like Bible times. Christ tells us in modern scripture: "whether by mine own voice or by the voice of my servants, it is the same."(D&C 1:38). While the LDS prophet speaks the mind, will, and word of God, LDS leaders to do not claim to be infallible.
The Lord uses imperfect men to lead His church. The same modern scripture that declares that the LDS Prophet speaks on behalf of God also talks about their weaknesses: "And inasmuch as they erred it might be made known" (D&C 1:25). We are assured that our leaders will never lead us astray, but that doesn't mean they are perfect and don't ever make mistakes.
The LDS Church has been recently addressing difficult issues from its past regarding polygamy and priesthood. There is nothing new here. LDS leaders are continually asked about these issues. When the revelation on priesthood was received in 1978, Elder McConkie said at the time "Forget what I or Brigham Young or anyone else has said which is contrary to the current light and knowledge we have now received. We spoke without understanding." Elder McConkie frankly admitted and apologized for his mistake. While the priesthood prohibition was a temporary necessity, the reasons Elder McConkie gave to defend the policy were admittedly mistaken.
In spite of the weakness of our leaders, it is a shame when any LDS member loses faith and abandons the Church, their covenants, and their faith over these issues. The LDS Prophet is like the pitcher on a baseball team. All the Church membership make up the rest of the team. Just because the pitcher throws a few balls or even a wild pitch, doesn't mean we should throw down our glove, storm off the field, and abandon the team over it. Even in spite of a few wild pitches and a handful of balls mixed with strikes, the pitcher can still be throwing a perfect game. And so it is with our LDS leaders. Also, we should remember that it is not our job to be calling balls and strikes but to play our position.
Another example of what I am talking about is found in the Old Testament. Israel was wondering in the desert and needed water. Moses was commanded to strike the rock. Moses struck the rock twice, which was a mistake. But in spite of Moses' weakness, the water still flowed. We have covenanted and God expects us to sustain our leaders even in their weakness. And, like Moses, we can have faith, hope and an assurance that notwithstanding the weakness of our leaders, the water will still flow.