Insights into what made it onto the plates

3 Nephi gives us a glimpse into what was recorded on the plates and what was not.  Consider these verses:

In 3 Nephi 23, Jesus gives us a commandment regarding the words of Isaiah:

1 And now, behold, I say unto you, that ye ought to search these things. Yea, a commandment I give unto you that ye search these things diligently; for great are the words of Isaiah.
2 For surely he spake as touching all things concerning my people which are of the house of Israel; therefore it must needs be that he must speak also to the Gentiles.

Later in the same chapter, Jesus commands the Nephites to record the prophecy and fulfillment of Samuel regarding saints being resurrected:

7 And it came to pass that he said unto Nephi: Bring forth the record which ye have kept.
8 And when Nephi had brought forth the records, and laid them before him, he cast his eyes upon them and said:
9 Verily I say unto you, I commanded my servant Samuel, the Lamanite, that he should testify unto this people, that at the day that the Father should glorify his name in me that there were many saints who should arise from the dead, and should appear unto many, and should minister unto them. And he said unto them: Was it not so?
10 And his disciples answered him and said: Yea, Lord, Samuel did prophesy according to thy words, and they were all fulfilled.
11 And Jesus said unto them: How be it that ye have not written this thing, that many saints did arise and appear unto many and did minister unto them?
12 And it came to pass that Nephi remembered that this thing had not been written.
13 And it came to pass that Jesus commanded that it should be written; therefore it was written according as he commanded.

In 3 Nephi 24 and 25, Jesus gives the Nephites the words of Malachi, which he later explains in 3 Nephi 26 is by way of commandment from the Father:

2 And he saith: These scriptures, which ye had not with you, the Father commanded that I should give unto you; for it was wisdom in him that they should be given unto future generations.

(Internal consistency note -- compare 3 Nephi 24:1 and 3 Nephi 26:1.  Jesus expounded these words after delivering them to the people.)

In 3 Nephi 26, Mormon tells us in an aside that he was about to write the 3 days worth of teaching Jesus gave the people, but was commanded not to write them to try our faith. And if we exercise faith in these words we will be given the greater things:

6 And now there cannot be written in this book even a hundredth part of the things which Jesus did truly teach unto the people;
7 But behold the plates of Nephi do contain the more part of the things which he taught the people.
8 And these things have I written, which are a lesser part of the things which he taught the people; and I have written them to the intent that they may be brought again unto this people, from the Gentiles, according to the words which Jesus hath spoken.
9 And when they shall have received this, which is expedient that they should have first, to try their faith, and if it shall so be that they shall believe these things then shall the greater things be made manifest unto them.
10 And if it so be that they will not believe these things, then shall the greater things be withheld from them, unto their condemnation.
11 Behold, I was about to write them, all which were engraven upon the plates of Nephi, but the Lord forbade it, saying: I will try the faith of my people.
12 Therefore I, Mormon, do write the things which have been commanded me of the Lord. And now I, Mormon, make an end of my sayings, and proceed to write the things which have been commanded me.

Jesus tells the Nephites that the world will be judged by the words that are written in this book in 3 Nephi 27:

25 For behold, out of the books which have been written, and which shall be written, shall this people be judged, for by them shall their works be known unto men.
26 And behold, all things are written by the Father; therefore out of the books which shall be written shall the world be judged.

What can we conclude from these insights? Here are a few key lessons I learn:

1. Jesus Christ is very aware of and concerned about what is in the record.
2. This concern seems to center on a desire to show that the words of the prophets are fulfilled. (This echoes what Mormon and other prophets say repeatedly in other parts of the Book of Mormon.  See this post for example.)
3. We will be judged out of the words which are written in the scriptures.
4. In offering the Nephites words of Malachi (an Old Testament prophet who lived after Lehi left Jerusalem), Jesus does not explain the context.  This suggests to me that these words transcend time and mortal context--if the Father commands that these words be given to us, they are given, if He commands that they remain hidden from us, we don't get them. This leads to my last point...
5. Faithfully receiving the words we have been given is more important than debating whether we should have them in the form we have them or not.  

Given the amount of debate that goes on about the nature of Isaiah quotations in the Book of Mormon, KJV translation anomalies, etc., I feel like how we approach this phenomenon is critical. Our approach determines how we receive these words.  The skeptical approach is to conclude that Joseph Smith was simply filling up volume with KJV passages and that the consensus of scholars conclude there is no way Nephi would have had access to some of the the passages he quotes, and that we can therefore reject the Book of Mormon. (As an aside, I believe seeking to understand these issues is wise, but if we conclude that we know better than God and choose to reject these words as a result of our study, we've gone too far.)

On the other hand, the faithful perspective allows us to receive these words with gladness and await the greater things that He promises to send us.

President Ezra Taft Benson spoke very directly and boldly about the purpose of the Book of Mormon in this sermon in 1986.  It is worth a read.