A few points that I found while doing a quick search around.
Joseph Smith said that six foot men, dressed like Quakers, live on the moon and live to be 1000 years old. (The Young Woman's Journal,Vol 3,p263)
Brigham Young claimed that men inhabit the sun. (Journal of Discourses, Vol.13, p.271, 10/24/1870)
Brigham Young also prophesied that the Civil War would not free the slaves.(Journal of Discourses, Vol.10, p.250, 10/6/1863)
I verified those three, I found this, but was unable to verify it:
Joseph Smith claimed that Jesus would return by 1891 (History of the Church,Vol.2,p182)
Also apparently scholars have looked at the Egyptian Papyrus that Joe Smith claimed to have translated and discovered to be the Book of Abraham, and it is largely the Book of the Dead, and other Egyptian burial text, and noting about Abraham.
A few good questions I came across:
Mormons believe that the Church that Jebus founded fell into total apostasy in the 1st century, yet the Bible as we know it wasn't compiled for at least another century by the Catholic Church and the King James Version of the Bible, which Mormons use, wasn't produced until the 17th century. Why do Mormons use the Bible at all, since, under their beliefs, it was compiled by an apostate church?
Doesn't it seem odd that the Mormon church followed the United States command rather than God's command? (e.g. Polygamy ended when challenged by the government and blacks were allowed to be priests following the civil rights movement.)
If Brigham Young was a true prophet, how come one of your later prophets overturned his declaration which stated that the black man could never hold the priesthood in the LDS Church until after the resurrection of all other races (Journal of Discourses, Dec. 12, 1854, 2:142-143)?
Can you show me archeological and historical proof from non-Mormon sources that prove that the peoples and places named in the Book of Mormon are true?
Why does the Book of Mormon state that Jesus was born in Jerusalem (Alma 7:10) when history and the Bible state that he was born outside of Jerusalem, in Bethlehem?
If the Book of Mormon is the most correct of any book on earth, as Joseph Smith said, why does it contain over 4000 changes from the original 1830 edition?
If the Book of Mormon was engraved on gold plates thousands of years ago, why does it read in perfect 1611 King James Version English?
If God was once just a man who progressed to becoming a God, how do you explain Psalm 90:2: “…even from everlasting to everlasting, thou art God”?
How can any men ever become Gods when the Bible says, “Before me there was no god formed, neither shall there be after me”? (Isaiah 43:10)
How can a man who is not a descendant of Aaron hold the Aaronic Priesthood? (Numbers 16:40)
How did Nephi with a few men on a new continent build a temple like Solomon's while Solomon needed 163,300 workmen and seven years to build his temple? (1 Kings 5:13-18 and 2 Nephi 5:15-17).
Why is it that numerous LDS books and papers describe proposed Book of Mormon locations for cities and the "narrow neck of land"? No city has been identified as being Nephite, Lamanite, Jaredite, etc. For example, Zarahemla was occupied for hundreds of years, but we still don't have any real evidence of it ever existing. The Book of Mormon describes a time period from 2000 BC to 400 AD and millions of people. No city they occupied has yet to be found.
Why are Greek names such as Lachoneus, Timothy, Jonas, and Alpha & Omega in a book that should have absolutely no Greek influence?
Why doesn't a linguistical relationship exist between any native American language and ancient Egyptian or Hebrew?
How did the Book of Mormon language evolve so rapidly into non-related Indian languages? Indo-European is much older than the Book of Mormon time period, yet vestiges of Indo-European exist through all of Europe and parts of Asia.
Why are only four main types of Mesoamerican writing systems known (and none in pre-Columbus North America): (Aztec, Mixtec, Zapotec, and Maya)?
Why haven't any of the Book of Mormon proper names such as Nephi, Laman, Zarahemla, etc. been found in all of the many writings that have been found in Mesoamerica?
Why aren't any of the Indian tribes racially or genetically the same as Hebrews? American Indians are all of Mongoloid origin.
Why is the Passover mentioned 71 times in the Bible, but -0- times in the Book of Mormon?
How did Book of Mormon characters get the priesthood when they weren't from the tribe of Levi?
Why does the Book of Mormon prophesy that the Jews would be restored to the land of their inheritance if they believed in Christ (they are occupying it now w/o believing in Christ)? (2 Nephi 10:7)
Why was Paul referred to before his time? (Paul said, "Death where is thy sting")
Why is a Greek word like "Christ" used throughout the Book of Mormon?