According to proponents of Sola Scriptura, what are examples of logical contradictions between doctrines from the Bible and LDS sacred books?

In addition to Anne's in-depth answer, I'll give a specific and important difference between what the Scriptures teach and what the LDS texts teach.

On the topic of salvation, 2 Nephi 25:23 states that

For we labor diligently to write, to persuade our children, and also our brethren, to believe in Christ, and to be reconciled to God; for we know that it is by grace that we are saved, after all we can do

Only "after all we can do" are we saved by grace, according to the LDS. But this is contrary to the Scriptures.

But God, being rich in mercy, because of His great love with which He loved us, even when we were dead in our wrongdoings, made us alive together with Christ (by grace you have been saved), and raised us up with Him, and seated us with Him in the heavenly places in Christ Jesus, so that in the ages to come He might show the boundless riches of His grace in kindness toward us in Christ Jesus. For by grace you have been saved through faith; and this is not of yourselves, it is the gift of God; not a result of works, so that no one may boast. (Ephesians 2:4-9)

But if it is by grace, it is no longer on the basis of works, since otherwise grace is no longer grace (Romans 11:6)

We see through the Scriptures that it doesn't depend on our works in the slightest, but the LDS holy text specifically requires our works. The Scriptures have our works coming as a result of our salvation, and not the other way around, which is contradicted in the LDS sacred books.

Keeping this brief, I'll just point out a couple of things. I'm a supporter of Sola Scriptura, Tota Scriptura (which is also called the plenary inspiration of Scripture) and in the divine preservation of Scripture. The Westminster Confession of Faith (written in 1646) states:

"The Old Testament in Hebrew... and the New Testament in Greek... being immediately inspired by God, and by his singular care and providence kept pure in all ages, are therefore authentical." (1.8)

Statements that are equivalent, if not identical, appear in the Savoy Declaration (1658), the Helvetic Consensus Formula (1675) and the London Baptist Confession (1689). The point in mentioning this is to flag up that whatever religious writings the Latter Day Saints came up with from the early 1800s onwards, many of their doctrines automatically clash with those Protestant statements of belief about divinely inspired and preserved Scripture stated 200 years earlier.

This means that the point of the argument of supporters of such Protestant declarations is that any religion coming along later to say "We have divinely-inspired holy scripture that adds to earlier divinely-inspired scripture", has already contradicted Sola Scriptura etc. Their very claim is a contradiction in terms!

Those who know what the Hebrew and Greek Scriptures say know that the final written word from God was that last book in the Bible, the Revelation of Jesus Christ, given in visionary and audible form to the elderly apostle John, before the end of the first century A.D. I am not going to trawl through a list of texts which show that. Anybody claiming to have divine revelation from God thereafter, which they say is equal to, or superior to, what is already in the Bible, must by definition contain some doctrines that absolutely clash with biblical doctrine. Upholders of Sola Scriptura know of examples of that with the LDS religion, but I for one am not going to spend a huge amount of my time detailing such contradictory doctrines.

My second, and fleeting point, is that many books written by LDS founders are swiftly relegated to non-inspired status when things in them that do contradict what the Bible states are pointed out. Yet the LDS religion continues to state in its articles of faith that the Bible is only inspired of God insofar as it has been correctly translated:

"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." Article of Faith No. 1.8

This then allows them to go by Joseph Smith's annotated version of the King James Bible. Helpfully (for them) Smith has noted what 'authentic' verses should have said. If they wish to take that approach to the Bible, they are free to do so, but they need not expect proponents of Sola Scriptura to pay heed to them, for the two groups stand in diametrical opposition, when it comes to many biblical doctrines.

I have already answered a related question over a year ago, What evidence does the LDS Church offer regarding claims of degradation of Biblical texts?

EDIT as requested: Additional example: The Jehovah of the Old Testament was created by the god Elohim and his wife as their firstborn spirit baby who later became the man, Jesus. But that's not in the Book of Mormon. And when quotes are made from the speeches / writings of the founding LDS members who taught it, denials come from LDS people. Then my second point is rolled out: “Oh, but those claims are of non-inspired status so it’s no use referring to them!” This may be viewed as a bit of a dodge by some, but this is what people can be up against when they point out an LDS belief that is in print, but which seems to directly contradict orthodoxly Christian, biblical doctrine. “This is not a doctrine!” comes the reply. It then turns into a futile argument which I have no intention of engaging in.

My already stated example (of LDS belief in needing extra-biblical literature and revelations) shows why those who believe in Sola Scriptura have problems with some LDS teachings / beliefs that are found in their extra-biblical literature, and why nobody can get anywhere trying to thrash that out. You asked for answers from believers in Sola Scriptura; let there now be another question asking for why LDS people reject Sola Scriptura. Readers can read both sides of the ‘case’ and weigh matters up for themselves.