Here are some things about Mormonism that many people do not know. Anyone who would like to learn more may use the valuable links on the thread: "Resources for those investigating all things LDS".
1) The Book of Abraham is not as Joseph Smith claimed - the writings of Abraham written by his own hand upon papyrus. In fact, the text contains anachronisms and much of the text appears to be borrowed from other authors whom Joseph confessed to be familiar with: Swedenborg, Book of Jasher, Josephus, Thomas Dick, etc.
2) Joseph Smith had 33 wives, at least one as young as 14, two were his own teenage foster daughters, and several were concurrently married to other men, and yes there is sufficient evidence (children and statements) that he had sex with many of them.
3) The text of the Book of Mormon was dictated by Joseph while burying his head in a hat with the very same peep stone he used while defrauding Josiah Stowell by claiming to be able to find buried treasure and accepting payment for those services.
4) Many of the doctrines and stories Joseph claimed were revealed to him from heaven were actually plagiarized from the writings of others that we have evidence he was familiar with: Swedenborg, the Book of Jasher, Josephus, Thomas Dick, Ethan Smith, etc.
5) Many supposedly eternal doctrines (aka unchanging truths) have been changed. For instance Brigham Young taught not only from the pulpit, but also arranged to be taught during the lecture at the veil that Adam is God the Father, the same one who sired Jesus Christ in Mary's womb, that Eve was just one of Adam's wives that he brought with him to start the human race on earth. Joseph Fielding Smith outright rejected that doctrine as false, but remember this had been taught quite clearly and unambiguously in the temple. Also the doctrine of blood atonement in which the only way to get forgiveness for certain sins is to have your life taken by church leaders who spill your blood on the ground was taught by Brigham, but is now denied.
6) The temple signs and tokens (and penalties) were lifted from the Masons. And the Masons and their signs date back to the 12th century AD not back to the building of the Jewish temples.
7) There is a history in the Church dating back to Joseph Smith in which the leaders have lied about their history and practices. Joseph "rewrites" his history several times embellishing accounts and changing the timing of things. The Church today slyly edits original quotes for its manuals to cover up the polygamy preached and practiced by its early leaders. But, worse than that, old Gordy Hinckley lied to police investigators about his involvement with Mark Hoffman and thus obstruction a murder investigation.
8) We have a lot of DNA evidence that shows that the Native Americans are not descended from Middle Eastern peoples. No archaeological support for BoM, despite what your institute teacher told you. The story of Thomas Ferguson might interest some of you as well as B.H. Roberts investigation into the Book of Mormon.
9) The Church has a nasty habit of excommunicating historians for telling the true history of the Church (i.e., September Six, etc). The Church has what is known as the Strengthening Church Members Committee whose job is to collect information on and writings of dissidents.
10) There are a handful of contradictory versions of Joseph's First Vision. None of these accounts were created until years after the supposed events would have taken place. In fact, all the early accounts always say that Joseph was called to the work by an angel, no one seemed to know anything about a "First Vision" in which Joseph saw God and Jesus. In fact, the idea that God and Jesus were two separate beings never occurred to anyone, not even Joseph, until sometime after the church was established. Joseph revised the first part of the Book of Mormon to make references to Jesus as the Son of the Living God as opposed to the "Living God". Joseph eventually abandoned his editing before he got to Abinidi's confusing speech.
There are many more issues, but the most important thing for any investigator is to look at the original sources for yourself. Don't trust the writings of critics or the church approved books without first consulting the original sources. The writings of the critics will cite their sources so that you will know where to look. Frankly, I find the writings of the critics to be more trustworthy than the writings approved by the Church.
Happy researching! The link at the top of this post has links for both critical and apologetic sites. We critics have no need to hide apologetic arguments, because when a person evaluates both sides, I think they will most often side with the critics. However, you will not receive such a fair and balanced approach from the church defenders. Often, they don't want you to read critical literature or at least will not link to it.