As noted in the OP, this is a very extensive subject. I'll offer a very high-level overview of key points, and then drill down specifically on one example.
The most well-known passages that form the basis of Latter-day Saint teachings on imperfections in the Bible are:
...because of the many plain and precious things which have been taken
out of the book [the Bible], which were plain unto the understanding
of the children of men, according to the plainness which is in the
Lamb of God—because of these things which are taken away out of the
gospel of the Lamb, an exceedingly great many do stumble... (1 Nephi
We believe the Bible to be the word of God as far as it is translated
correctly; we also believe the Book of Mormon to be the word of God.
(Articles of Faith 1:8)
(note also that Joseph Smith regularly used the word "translated" the way 21st century English uses the word "interpreted")
How are plain and precious truths lost?
I'll give three methods that I am aware of--that doesn't mean there aren't more, just that there are three with which I am familiar.
Changes to the Biblical text. This one gets talked about the most and is, IMHO, the least impactful of the three. That there are hundreds of thousands of variants in the Biblical text is well-established--see even just the links in the OP--but the overwhelming majority have no impact on our ability to understand the text.
One example of a textual variant that I do consider doctrinally significant is Luke 22:44--I do believe that Jesus' bleeding in Gethsemane was a real phenomenon and is of theological significance (see also Mosiah 3:7)
Changes to meanings of words. In this case the words themselves are faithfully handed down, but the meanings associated with those words changes, which can cause significant doctrinal variation. I suggest words like "grace", "saved", and "spirit" fit this category. I'll discuss grace in more detail below.
Knowledge not handed down. There were things known by Moses, Melchizedek, Peter, Paul, etc. that didn't make it into the Bible, either because they were never written down, or because they were written but lost before OT or NT texts were compiled (e.g. 1 Cor. 5:9)
The Latter-day Saint position on this is:
We believe all that God has revealed, all that He does now reveal, and
we believe that He will yet reveal many great and important things
pertaining to the Kingdom of God. (Articles of Faith 1:9)
We are open to any truth God has spoken in the past or will speak in the future, regardless of whether or not it has a pedigree in Jewish literature or the writings of early Christian fathers.
The Joseph Smith Translation
The introduction to the Joseph Smith translation indicates that its purpose is to restore truth. It's purpose is not to restore the autographical texts of the Bible. To be just a touch humorous while also making this point, let us consider...the autographical texts of the Bible were written in Hebrew, Aramaic, and Greek. The Joseph Smith translation is in English, and is therefore not a verbatim copy of the autographs.
I'll briefly outline 4 purposes I have found (in my own study) of the Joseph Smith translation:
- To clarify vague passages (e.g. Luke 23:34)
- To restore original message (e.g. John 4:24, the JST does not go into the debates on the meaning of Πνεῦμα ὁ Θεός but rather focuses clearly on the principle being taught to the Samaritan woman)
- To restore knowledge once had (e.g. the Book of Moses)
- To guard against false doctrine (e.g. 1 Cor. 14:34-35, women are most certainly permitted to speak in The Church of Jesus Christ of Latter-day Saints)
A specific example--grace
The Church of Jesus Christ of Latter-day Saints holds that the principle of "grace" as taught by Luther, Calvin, and others is doctrinally & historically incorrect. I say this not to insult anyone but to acknowledge what we believe.
I have produced several YouTube videos on the meaning of "grace" (here and here)
I am particularly appreciative of the work by Greek scholar Brent Schmidt on the meaning of the Greek word "charis". Relevant academic discussion can be found here, here, and here.
In short, grace does not describe a free gift. It is a gift that comes with obligations. In the time and culture of Paul, "charis" was
- An asymmetric, reciprocal gift relationship
- A covenant
To put it into my own, theologically crude, words: grace sufficient for salvation is dispensed through the ordinances and covenants of the Gospel of Jesus Christ. Failure to participate in those ordinances and covenants prevents access to portions of God's grace. We are given what we could never earn, but we play a role in this covenant relationship.
As explained more eloquently by Moroni:
32 Yea, come unto Christ, and be perfected in him, and deny yourselves
of all ungodliness; and if ye shall deny yourselves of all
ungodliness, and love God with all your might, mind and strength, then
is his grace sufficient for you, that by his grace ye may be perfect
in Christ; and if by the grace of God ye are perfect in Christ, ye can
in nowise deny the power of God.
33 And again, if ye by the grace of God are perfect in Christ, and
deny not his power, then are ye sanctified in Christ by the grace of
God, through the shedding of the blood of Christ, which is in the
covenant of the Father unto the remission of your sins, that ye become
holy, without spot. (Moroni 10:32-33)
This then would be a case where, in a Latter-day Saint worldview, the Biblical words were preserved, but the meaning was not.
For those interested, the loss of plain and precious truths is specifically discussed in this video on my channel.
It is sometimes asserted that Latter-day Saints mistrust the Bible. I personally am saddened by this rumor, because I am an avid student of the Bible. My area of study is the Synoptic Problem and I have spent a great deal of my research arguing for the high degree of reliability of the Synoptic Gospels.
Disclaimer: these comments are products of my own study and do not constitute official statements of The Church of Jesus Christ of Latter-day Saints