The Mormons tells a story of persecution that I don't think most Americans are aware of with respect to the Church of Jesus Christ of Latter-day Saints. Joseph Smith and his followers - and later Brigham Young - were basically chased across the country for their beliefs. They left New York, then got chased out of Missouri when they claimed it was a sacred site. Smith was killed by an angry mob in Nauvoo, Illinois. Brigham Young's church was essentially outlawed by the United States Congress. The church has suffered an immense amount of persecution in its short history.
The other side of the church's short history, is that the revelations that serve as the basis for church doctrine do not have thousands of years to shield them from skepticism. Smith began his movement in what the documentary claims was a time and place that was ripe for religious men like Joseph Smith. Though Smith's beliefs are no more miraculous than those of Christianity, he clashed with most established denominations and was forced to flee.
Persecution also goes the other way as well, with the church having to reform itself of its racist ways, but still not giving women the same rights as men in the church, and still not giving respect to homosexuals.
Some other take away points:
The documentary also touched on how church doctrine - plural marriage, for instance - was developed through "revelation".
Like most religions, the church functions as a community as well as a spiritual center. It is also active in charitable works.
Mormons are required to go out on missions to evangelize the faith across the world. There's a somewhat funny part where two Mormon men try to evangelize New Yorkers on the street.
The Mormons have a somewhat controversial practice of baptizing the dead, even if the dead person was not a Mormon. This upset Jews who feel the Jewish people have fought to remain Jewish throughout their history.
The Mormon temple is a secretive place that is off limits to non-Mormons and even Mormons who don't live by the strict codes of the church.