There have been no changes at all to the Doctrine of Christ since the very beginning of the Church of Jesus Christ, which was first established on this Earth through Adam, the first man, and the first prophet also on the face of it. However, there have been numerous periods of apostasy, when the understanding of that doctrine was not had by any mortal on the face of the Earth. The same pattern applies today: We learn about the same doctrine of Christ as was preached in the Old and New Testaments, as well as through the newer and additional testaments (A better translation for the word "Testament" here is Covenant), yet the variability of our understanding does not modify the Lord's doctrine, which is eternal. The Lord reveals the things of His kingdom both to the church generally, and to His children individually, incrementally. Therefore the pattern we are perceiving is not one of "changes" to the doctrine, but rather, changes in the extent to which we perceive His doctrine and His plan. In a word, revelation.
I know of no exact metric for determining whether or not a given revelation ought to be canonized except that the Prophets and Apostles propose additions to the canon by revelation from Jesus Christ (just as Peter and Paul received revelations which were later canonized) and they are accepted as such by the law of common consent by the members of the church. In truth we are to "live by every word that proceeds from the mouth of God", whether by the Prophet (with a capital P) or by the gift of prophecy among the body of Christ more proximally (lowercase p). All that is inspired of the Holy Ghost is of God, and we will be judged accordingly.
The Doctrine of Christ is the only doctrine of the Church of Jesus Christ of Latter-day Saints; we have no other doctrine. All Scripture attests to this fact. It has not changed a jot or a tittle since before this world was made, through all the prophetic dispensations. (I speak for myself only, with my own views and testimony, I am not a spokesman for the church).
The Doctrine of Christ
And the Father said: Repent ye, repent ye, and be baptized in the name
of my Beloved Son. And also, the voice of the Son came unto me,
saying: He that is baptized in my name, to him will the Father give
the Holy Ghost, like unto me; wherefore, follow me, and do the things
which ye have seen me do. [Have] faith in [Christ] ... This is the doctrine of Christ. (2 Nephi 31:11-12,19,21)
The degree to which a person understands the Doctrine of Christ is a variable. God's plan of salvation is deeply nuanced, and it is impossible to for mortal man to find out all his ways, yet God gives revelations to man through His prophets and personal revelations by the power of the Holy Ghost precisely for the purpose of bringing His children back into His presence, by redeeming and sanctifying them to the extent they are willing and do His will. God reveals commandments to His children line upon line. Because He has given us commandments, taught principles, or even expounded doctrine in the past, does not mean that He cannot now or in the future give us more commandments, teach us more refined principles, or expound the doctrine further. It is the same doctrine all in all, though our understandings change, His doctrine has never changed, and is the same from all eternity to all eternity.
Policy changes, commandments, revelations
All else, that is, the opinions about why a given policy began or ended, or those policies themselves, or the institution of a new commandment by the Savior to His church, does nothing to change doctrine.
There have been policy changes, which follow what I call "The bathtub principle" of revelation.
A mother asks her son to go and fill the bathtub. This requires stopping the drain and turning the faucet to let water in. Later, the same parent asks her son to stop filling the bathtub (because it is full!). A short-sighted person will say the mother is being inconsistent. In reality the policies and practices of the Living Church of the Living Christ must change depending on the conditions of man and are calculated for his salvation and exaltation, yet the doctrine is eternal.
The law that the Lord gave to Moses followed this pattern. There was a time and a place for it, and the Lord was indeed the Giver of it, but the more important loyalty is to the Lord Himself, not to the temporal, that is, the temporary precepts and practices. Nonetheless the Lord requires a willing heart and mind, and our choice to obey Him regardless of the task brings us unto His power of Atonement.
This is the doctrine of Christ: that through the Atonement of Christ, all mankind may be saved by obedience to the laws and ordinances of the Gospel. The first principles and ordinances of the Gospel are, first, faith in the Lord Jesus Christ, second, repentance, third, baptism by immersion for the remission of sins, fourth, the laying on of hands for the gift of the Holy Ghost. It has always been so. How far those laws and principles are revealed in a given dispensation, or the degree of an individual's understanding of the infinite scope of His vast plan for our happiness, changes nothing in terms of the doctrine. It has never changed; it was made by the unalterable decree of God since before this world was. The dishonest will claim that this is some "new doctrine", but they err, having not understood the doctrine of Christ which was before made known to them by the Scriptures. It is the same doctrine as has always been preached by Prophets and Apostles of Jesus Christ, and by the Lord Himself.
In summary, there has never been a change of doctrine in the Church of Jesus Christ, from Adam to Enoch to Noah to Abraham to Moses to Jesus in the meridian of time, to Joseph Smith, to the present-day prophet President Russell M. Nelson. Temporal commandments have come and gone, and policies and procedures have been swapped out and amended by revelation from Jesus Christ, just as circumcision was at first installed and later revoked by the Lord Himself. The laws are eternal, the principles are sure, and the doctrine is forever. "Though the heavens and the Earth shall pass away, [His] word shall not pass away, but shall all be fulfilled." He guides the Church today as He has in the past. This is the doctrine for which all men who ever lived or who ever will live will be held to account before the Judgment Bar of the Almighty God. All the Prophets bear witness of this doctrine, that is, the Doctrine of Christ, that a man must repent and come unto Christ, or he cannot be saved.