First of all, we should notice the important difference between the Nephi version and the Matthew version. To the Nephites he declared that they should be perfect even as I or your Father is perfect. Although Jesus of Nazareth was the only sinless individual, when he delivered the Sermon on the Mount he had not yet been glorified and resurrected. For this reason, and for the sake of humility, he did not include himself as being perfect.
Whenever a discussion of perfection comes up, someone is always quick to point out that we cannot become perfect while in mortality. Yet, the Savior gives us a commandment that must somehow be fulfilled, for the Lord giveth no commandments unto the children of men, save he shall prepare a way for them that they may accomplish the thing which he commandeth them (1 Nephi 3:7). Is perfection attainable in mortality? The answer is a qualified "yes."
James E. Talmage said, "Our Lord's admonition to men to become perfect, even as the Father is perfect (Matt. 5:48) cannot rationally be construed otherwise than as implying the possibility of such achievement. Plainly, however, man cannot become perfect in mortality in the sense in which God is perfect as a supremely glorified Being. It is possible, though, for man to be perfect in his sphere in a sense analogous to that in which superior intelligences are perfect in their several spheres; yet the relative perfection of the lower is infinitely inferior to that of the higher." (Jesus the Christ, p. 232)
A careful reading of the scriptures demonstrates that three individuals are referred to as "perfect": Seth (DC 107:43), Noah (Gen 6:9), and Job (Job 1:1). To be perfect in this scriptural sense means to be complete, finished, or fully developed. Seth, Noah, and Job (and probably scores of other prophets) had become perfect in the scriptural sense. They had learned to serve God with a perfect heart and with a willing mind (1 Chron 28:9). They had submitted their wills to the will of the Father. This was the quality the Savior wished for the Twelve, that they may be one, even as we are one: I in them, and thou in me, that they may be made perfect in one (Jn 17:22-23, italics added).
Yet, all have sinned and come short of the glory of God (Rom 3:23). But in Christ the sinner is perfected, the debt is paid, and the dirty are made clean. This is why the Savior prayed that the Twelve would be made perfect in one. Through Christ, we attain "scriptural" perfection when our will is the same as the will of the Father. This can occur prior to the resurrection, for Joseph Smith spoke of certain angels who are the spirits of just men made perfect, they who are not resurrected, but inherit the same glory (DC 129:3). Our goal is to strive to perfect ourselves, carefully aligning our thoughts and desires with God's, that we may be made perfect in Christ and inherit the same glory.
Bruce R. McConkie
"Finite perfection may be gained by the righteous saints in this life. It consists in living a godfearing life of devotion to the truth, of walking in complete submission to the will of the Lord, and of putting first in one's life the things of the kingdom of God. Infinite perfection is reserved for those who overcome all things and inherit the fullness of the Father in the mansions hereafter. It consists in gaining eternal life, the kind of life which God has in the highest heaven within the celestial world." (Mormon Doctrine, p. 567)
The Sermon on the Mount as taught in 3 Nephi differs in many instances from the same sermon as recorded in Matthew 5-7.To help the reader identify the differences, the text from the Book of Mormon version which differs from the Matthew version will be highlighted in blue text, while the text which is the same as the Matthew version will be highlighted in red text. For example, Matt 5:3, reads, "Blessed are the poor in spirit…," while the 3 Nephi version reads "Yea, blessed are the poor in spirit who come unto me…" Therefore the 3 Nephi version will be represented as follows, Yea, blessed are the poor in sprit who come unto me. If you're color-blind, I apologize.