As I explained in a previous post, The Trinity, Historic Christianity believes in the Trinity. In a fundamental difference with Historic Christianity, Mormons reject the Trinity. Instead, Mormons believe in the Godhead, composed of Three Gods, God the Father, God the Son (Jesus Christ), and God the Holy Spirit. Though they are three separate and distinct Gods in their own right, they work in unity through the Godhead, with God the Father as the primary God in charge.
The Mormons believe the Nicene Council (325 A.D.) fabricated the teaching about the Trinity out of whole cloth. This position ignores the numerous statements throughout the Old Testament and extending into the New Testament that there is only One God. It ignores the implied teachings about the Trinity in the New Testament. It also ignores the numerous statements of early Church fathers about the Trinity, including those who had been alive when the apostles were still alive.
I haven't yet found a Mormon who can adequately explain all this. They will talk about how One God refers to only the Father, or only the Son, though those terms are not used in the Old Testament. Or they will insist that the Hebrew word Elohim refers to the Father, and Yahweh or Jehovah (an English transliteration of Yahweh) refers to the Son, even though these terms are all used interchangeably for God in the Old Testament. They especially have problems if you point out the combined Hebrew word which is translated Yahweh Elohim.
On a philosophical level, Three Gods would not lead to unity, even if it is claimed they work together, and eventually lead to disunity. The Mormons pride themselves on a unified religion, which they have as long as you do not seriously question the leadership publicly. (Those who do have been excommunicated.) However, the Mormon Church is one denomination among several in the Restorationist movement (all who believe Joseph Smith was a prophet and the Book of Mormons is a new revelation from God) and none of those denominations even talk to each other. In addition, the Mormon Church has led to one of the deepest divisions with every Christian denomination or church. The Mormons hold all of them to be apostates (a word essentially synonymous with rebellious). They agree that both Jesus Christ and God the Father told Joseph Smith in the First Vision (according to his third written account in 1938) that all Christian churches were wrong. (The two earlier written versions before did not mention that all the Christian churches were wrong, or that both Jesus and the Father appeared to Joseph Smith.) Oddly, while the Mormons desire the respect of other Christians, they say all of them are apostates. Calling Christians apostates hardly leads to respect or unity.
It's a shame, because there are many shared values between Christians and Mormons, and I hope efforts can be made to focus on those shared values and to find areas to work together.