Mormonism has the most circular logic I've seen. Joseph Smith was the prophet because his church happened to thrive and do well and because the church does well it means he must have been the prophet. Not everyone in the world knows or understands Mormonism so everyone must know and understand through worldwide missionaries. Every religion aside from Mormonism is wrong because those religions only got a small part of God's message, so their existence proves that Mormonism has the complete picture. Christianity has so many sects because the church fell into apostacy, and the Mormon church has the true word because there are so many differing sects in the world. Any errors in Joseph Smith's lifetime are attributable to human fallacy, but the spiritual message is what matters, so criticizing the human aspect means nothing. Bringing up any contradictions, negative points, or errors in church history and doctrine is merely being "anti-Mormon" and is not focusing on the important, positive aspects that the church is all about. If the church makes any changes to its doctrines or policies it's because those changes were ordained by God to the current prophet. Electing someone "prophet" isn't illogical because God wants the vote to to turn out the way it does.

There are a ton of arguments you can make against Mormonism, but it doesn't mean its followers will listen. More arguments against it are countered with further "reasoning," delusions, and excuses that ultimately lead to "Mormonism has to be right because I believe it's right." Pointing out weird facts and discrepancies doesn't phase anyone, it just makes them label the arguer "anti-mormon" and leave it at that. People can get out of the religion if they research enough and have enough doubt in their religion, but this is a very personal thing and there are more people being preached to than there are people leaving the church.

Check out some of the influence on Wikipedia. Nearly every argument against a Mormon idea is countered with a "but" or "it could be explained" or "perhaps" rather than a simple acceptance of stated facts, while Mormon beliefs are stated as facts rather than beliefs, and myth is stated as actual history. Worse is when a Mormon "scholar" or "scientist" muddies up the facts with speculation. Cleanup is needed on a lot of these, as well as the template "This article or section may fail to make a clear distinction between fact and fiction."

http://en.wikipedia.org/wiki/Archaeology_and_the_Book_of_Mormon

http://en.wikipedia.org/wiki/Genetics_and_the_Book_of_Mormon

http://en.wikipedia.org/wiki/Golden_Plates

http://en.wikipedia.org/wiki/Plates_of_Nephi

http://en.wikipedia.org/wiki/Record_of_the_Nephites

http://en.wikipedia.org/wiki/Sword_of_Laban

http://en.wikipedia.org/wiki/The_Book_of_Mormon

http://en.wikipedia.org/wiki/Linguistics_and_the_Book_of_Mormon

http://en.wikipedia.org/wiki/Chiasmus_in_the_Book_of_Mormon

http://en.wikipedia.org/wiki/Nephite

http://en.wikipedia.org/wiki/Lamanites

http://en.wikipedia.org/wiki/Reformed_Egyptian

http://en.wikipedia.org/wiki/Urim_and_Thummim

http://en.wikipedia.org/wiki/Ancient_astronaut_theories

http://en.wikipedia.org/wiki/Book_of_abraham

http://en.wikipedia.org/wiki/Kolob

http://en.wikipedia.org/wiki/Sealing_%28Mormonism%29

http://en.wikipedia.org/wiki/Blacks_and_the_Latter_Day_Saint_movement

http://en.wikipedia.org/wiki/Adamic_language

http://en.wikipedia.org/wiki/Adam_and_Eve_%28Mormonism%29

http://en.wikipedia.org/wiki/Accounts_of_pre-mortal_existence

http://en.wikipedia.org/wiki/Celestial_kingdom

http://en.wikipedia.org/wiki/Great_Apostasy#The_Church_of_Jesus_Christ_of_Latter-day_Saints

http://en.wikipedia.org/wiki/Outer_darkness

http://en.wikipedia.org/wiki/Zion_%28Mormonism%29

http://en.wikipedia.org/wiki/Plan_of_salvation

http://en.wikipedia.org/wiki/Revelation_%28Latter_Day_Saints%29

http://en.wikipedia.org/wiki/Restoration_%28Latter_Day_Saints%29

http://en.wikipedia.org/wiki/Sealing_power

http://en.wikipedia.org/wiki/Seer_stone_%28Latter_Day_Saints%29

http://en.wikipedia.org/wiki/Continuous_revelation

http://en.wikipedia.org/wiki/Transgression_%28Latter_Day_Saints%29

http://en.wikipedia.org/wiki/Moroni_%28prophet%29

http://en.wikipedia.org/wiki/Moroni

http://en.wikipedia.org/wiki/Word_of_Wisdom

http://en.wikipedia.org/wiki/Quorum_of_the_Twelve_Apostles_%28LDS_Church%29

http://en.wikipedia.org/wiki/Seventy_%28Latter_Day_Saints%29

http://en.wikipedia.org/wiki/Apostle_%28Latter_Day_Saints%29

http://en.wikipedia.org/wiki/Prophet%2C_seer%2C_and_revelator

http://en.wikipedia.org/wiki/Nephi

http://en.wikipedia.org/wiki/Lehi_%28Book_of_Mormon_prophet%29

http://en.wikipedia.org/wiki/Mormon_%28prophet%29

http://en.wikipedia.org/wiki/Moronihah

http://en.wikipedia.org/wiki/Captain_Moroni

http://en.wikipedia.org/wiki/Zoram

http://en.wikipedia.org/wiki/Mosiah

http://en.wikipedia.org/wiki/Lost_116_pages

http://en.wikipedia.org/wiki/The_Book_of_Mormon_and_the_King_James_Bible

http://en.wikipedia.org/wiki/Cumorah

http://en.wikipedia.org/wiki/Bountiful_%28Book_of_Mormon%29

http://en.wikipedia.org/wiki/Ordinance_%28Mormonism%29

http://en.wikipedia.org/wiki/Endowment_%28Mormonism%29

http://en.wikipedia.org/wiki/Mormon_missionaries

http://en.wikipedia.org/wiki/Latter-day_Saint_theology_and_Judaism

http://en.wikipedia.org/wiki/Mormon_view_of_the_House_of_Joseph