The Church of Jesus Christ of Latter-day Saints has certainly seen its share of criticism. Whether it be criticism of the Church's stance on blacks and the Priesthood, or maybe even Baptisms for the dead, or perhaps it's the Church's stance on Gays getting married (click through those links to get a good overview of what those are). The "Mormon Moment" is bringing to the forefront issues that, while perhaps minuscule compared to other mainstream religious histories, due to a Mormon President running for Public office in the United States are now a mainstream issue.
There's one criticism I keep seeing though, which is that the Church has made "mistakes" in the past. That its leaders have swayed from what's "right", and some even suggesting that "The Church can't be true" because of those imperfections of its members and leaders. I'd like to make a bold statement saying, based on my own experience, any statement to that regard simply isn't true. It can't be as long as I call myself "Mormon".
I mentioned before that saying "I'm a Mormon" is a very bold statement. It truly is. It's saying that regardless of imperfect people guiding and leading the Church, this Church is still lead by God (you'll want to read that link). It holds His Priesthood, and He will not let it fall astray. Being a Mormon means, regardless of the imperfections of man, those men still receive revelation from God (I imagine some times whether they want it or not), some times revelation even they don't understand, and this Church is lead by HIM. Most of these men never asked for this calling - I'm sure they'd happily give it away if they didn't have such a firm conviction in God and this principle. To me, the Church of God CANNOT be true without imperfect men receiving revelation from Him to take His Gospel to the world. God will not allow His Church to fail - it's that simple. That's a very bold statement.
Mormons believe in the Atonement of Jesus Christ. We believe that mankind was brought to this earth because they were imperfect and needed to learn the things that would make it possible to live in the presence of our Heavenly Father. Christ came to this earth as the only perfect man, willing to give us the example, and take on our sins so that our sins would not hamper us down from moving forward to that end goal.
To a Mormon, God's Church cannot exist without imperfect people. It simply can't. At the same time it cannot exist without the Lord at the helm, leading the way with those called individuals as his mouthpiece. To Mormons, it could be any one of us called to that position, so we support these individuals with every bit we can, knowing and understanding the challenges they must be going through in order to fulfill such a solemn calling. (The story of Moses comes to mind, as does Joseph of Egypt and even Muhammed and other faiths' religious leaders and prophets throughout time that were average people, called of God in very humbling circumstances to be the mouthpiece of their God)
To suggest that anything ever happened to the Church, as a whole, was not lead by the Lord Himself, would completely discredit any truthfulness of The Church of Jesus Christ of Latter-day Saints. That is why the Church answers "we don't know" to questions such as blacks and the Priesthood - we simply don't know why the Lord wanted it that way. History shows that many leadership didn't want it that way, but the Lord still said, very directly, "No". And the truth is, we say that not because we're justifying the lack of revelation, but because revelation itself is guiding that response. When the Church says "we don't know", so does the Lord.
To suggest that "the Church made a mistake" on something as big as withholding the Priesthood from blacks simply can't be true if The Church of Jesus Christ of Latter-day Saints is to be true. The truth is, as Mormons, we believe this Church is true. We've each learned that through personal revelation (and we seek it if we don't yet have it), and because of that we cannot deny the fact that this Church was, still does, and will continually be lead by God Himself in the future. We don't always know why. We sometimes don't always understand and in many typical scenarios we'd even disagree (such as blacks and the Priesthood). However, this is HIS Church in every definition to Mormons and because we believe it's true, we follow the Lord's counsel.
Now it comes down to understanding yourself if God exists, if this is His Church, and if he speaks through prophets. None of this will ever make sense until you are able to come upon this yourself. It's a moot conversation until you do, and shouting from the housetops will never fix that.
Disclosure: as an employee of The Church of Jesus Christ of Latter-day Saints, these are my opinions and words, and not intended to be the voice of the Church. It's how I define my very personal testimony as a Mormon, and who I am. To learn from the voice of the Church and its called leaders, I encourage you to click through to the links throughout the article.