When refuting mormonism, it is difficult to choose which heresies to begin with. Why is this? Because you are truly being forced to refute more than simply one religion or world view.
When you look at what mormonisms teachings are, it is more than simply one religion, and requires an understanding of more than one religion. For instance, mormonism contains the following:
1 - Evolution - The mormon doctrine does not believe in creation ex nihilo (out of nothing). They teach that matter is eternal, and that it cannot be created. Now this is not to say that mormons believe in evolution as in the, "monkeys to man", but that they borrow a piece of what they believe from it.
2 - Universalism - This is the believe that people are inherently good, and almost all will be saved, regardless of if they believe in mormonism and hold to its teachings or not. They do not believe that all will be saved, but again, they borrow a piece from its concepts.
3 - Masonry - It is no secret that Joseph Smith was a mason, and many of the temple ceremonies have masonic elements, as well as the temples being full of masonic symbols. They do not necessarily teach all of the tenants of the masonic lodge, but they borrow from bits and pieces of it.
4 - Christianity. The momon founder Joseph Smith stole and plagiarized huge sections of the Bible when writing his book of mormon. The church today borrows many of the Christian terms, however, they change the definition entirely. They claim to have a love for the Bible, all the while insisting it is a corrupted, mistranslated book, that required restoration.
5 - Paganism - We see certain pagan elements to mormonism. This is to say that mormon doctrine borrows from such elements, such as baptism for the dead, which is a pagan practice. Again they do not borrow from all aspects of paganism, but only a part.
6 - Polytheism. This is the belief in multiple gods. Mormon doctrine is clear that their are "gods without number" and "worlds without number". While they say Jesus is the only god we (mormons) worship, they believe that not only is there an innumerable amount of gods, but that they themselves also can become gods.
7 - quasi-Gnosticism. (this from my friend Letitia) This is the belief in certain dualities inherent in the universe that unite to 'give birth' to certain other emanations. This is reflected in the doctrine stressing t...he need for male and female in ...the celestial world to produce spirit offspring and perpetuate a certain cycle of life. This is also reflected in the idea that Satan exists as necessary a being as God is (not my words but the missionaries!). Furthermore, it is reflected in the idea that we must 'return to Heavenly Father' as Mormons say, back to the source to shed our mortal bodies and enter a higher (exalted) state of being.
When dealing with mormonism, it is very helpful to have an understanding of all of these areas, however if you know your Bible, you will easily spot the false the doctrine.
Hopefully this has given my Christian friends some insight as to why it can be tricky to understand mormon doctrine, if your new to dealing with the LDS religion.