According to LDS, what principles of the gospel were corrupted in the Great Apostasy In the LDS.org article on Apostasy, the Great Apostasy is described in the following terms:

After the deaths of the Savior and His Apostles, men corrupted the principles of the gospel and made unauthorized changes in Church organization and priesthood ordinances.

Leaving aside the second part of the equation dealing with Church organization and priesthood ordinances, how exactly do Latter Day Saints believe the principles of the gospel were corrupted?
By way of background: I've had a couple of conversations with LDS (current or former missionaries) over the last year or so, where they have sought to emphasize the broad agreement with essential beliefs with other Christians. I find it hard to reconcile this with the LDS doctrine about the Great Apostasy and am trying to understand what they really meant. Is a de-emphasis of fundamental soteriological differences recommended as part of engaging with other traditions, or is the view on the &quot;Great Apostasy&quot; that is not that significant with regard to an understanding of the fundamentals of soteriological doctrine?
Within Mormon (LDS) theology, you can't speak of Church organization without speaking of priesthood authority.  The Priesthood exists without the Church but the Church cannot exist without the Priesthood.  The Priesthood is the power and authority given by God to act in the name of Jesus Christ.  So it makes no sense to a person of the LDS faith to separate the two.

But the question was what specific principles of the gospel were corrupted.  I would have to begin with the idea that God the Father and Jesus the Christ are of one substance (homoousia) which was cemented for Christiandom by the Nicene Creed (first council of Nicea in 325).  That is a major departing point from what a Mormon would believe is a correct principle of the Gospel.  Mormons believe that God the Father, Jesus Christ and the Holy Ghost (Spirit) are three distinct beings with one purpose.  Jesus Christ and the Holy Ghost are not the same being as God the Father, who is our only God.

Another difference that is more subtle is in regards to soteriology.  While Mormons agree that all humankind is freely given grace by the death and resurrection of Jesus Christ (the atonement) as do most Christians, Mormons believe that obedience to the laws and ordinances (saving works done under priesthood authority, such as baptism) of the gospel is also required.  Some Christians would say that God approaches humans with God's saving works and never the other way around.  Mormons believe that some effort is required by humans to receive this approach (free will and choice).  This does not change the fact that Jesus Christ is the bridge between God and humankind and nobody can return to the Father any other way.

Other important principles that have experienced a slow departure over the years of the  Church would include the following ideas, not all of which are opposed by all denominations of Christians.  Humans are not born sinners because of the Fall of Adam, and thus are judged for their own sins.  Mormons do not feel that babies require baptism.  Baptism is required through proper Priesthood authority when a person is capable of understanding and accounting for their own choices.  And finally, and probably a major point of irritation to many, the words of the Bible are not the final words of God.  Prophecy and revelation are still alive and present in the world.  God has not finished speaking to humans.

This is not all-inclusive, and I'm sure there are many more points that are perfectly good and important, but this is the list that expresses the areas of greatest concern among my fellows at the (Presbyterian) seminary I attended.