Does any of the LDS extra-biblical holy books ever clearly contradict the Bible?

No, not so far as the Bible is translated correctly. At the points where the Bible translation is not correct, it often contradicts itself, such as when a skewed translation claims that "it repented God that he had made man on the earth", yet in Numbers we read that God cannot repent because He is not subject to sin.

The Joseph Smith Translation (also called the Inspired Translation) corrects many of the errors in the degraded translations of the Bible, but as I understand it this inspired retranslation was never completed. You can find many instances where the Joseph Smith translation corrects or clarifies one of these scribal or other errors. The footnote on Genesis chapter 6 verse 6 is an example; the JST says that it was Noah who had those feelings, not God. The effect of the inspired translations of Joseph Smith is not only to expound the doctrine of Christ which is in the Bible, but they also correct some of the errors that have arisen in our renditions of it.

The Doctrine is the Same

Although names, places and events differ, the doctrine of Christ delivered in the Book of Mormon is self-consistent and completely consistent with the doctrine of Christ as revealed in the Bible:

"And he said unto the children of men: Follow thou me. Wherefore, my beloved brethren, can we follow Jesus save we shall be willing to keep the commandments of the Father? 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." (2 Nephi 31:10-12)

"And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit." (Acts 2:38)

Having both of these witnesses, it is not possible to miss noting what the doctrine of Christ is, and the central message of the Bible becomes all the more clear. It is not a travelogue for the Jews. It is an actual testament of the divinity of Jesus Christ, and that all men must come unto Him or they cannot be saved. The message of the Book of Mormon is the same.

The Book of Mormon fulfills prophecy made in the Bible, that God would send additional witnesses of His word, and that His word would become as one in our hands:

"Behold, I will take the stick of Joseph, which is in the hand of Ephraim, and the tribes of Israel his fellows, and will put them with him, even with the stick of Judah, and make them one stick, and they shall be one in mine hand." Ezekiel 37:19

The people of the Book of Mormon are descendants of Joseph.

"In the mouth of two or three witnesses shall every word be established" 2 Corinthians 13:1

Everyone is invited to read the Book of Mormon and enjoy its numerous confirming witnesses of the Bible, the promises of the Lord to His people and additional teachings of Christ intended specifically for our benefit in this day. He is the Living God and His words never cease; His work is ongoing today. Those who seek Him will find him, just as Nephi and Moses did, who are the first authors in each of these respective mountains of testimony that span generations and transcend nations.

Using only the Latter Day Saints own Book of Mormon, I would suggest contradictions here.

2 Nephi 25:23 - "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."

Cf. Romans 11:5-6 - "...there is a remnant according to the election of grace. But if it is by grace, it is no longer on the basis of works; otherwise grace would no longer be grace."

Alma 7:10 - "And behold, he shall be born of Mary at Jerusalem, which is the land of our forefathers, she being a virgin, a precious and chosen vessel, who shall be overshadowed and conceive by the power of the Holy Ghost, and bring forth a son, yea, even the Son of God."

Cf. Micah 5:2 - "But thou, Bethlehem Ephratah, thou be little among the thousands of Judah, yet out of thee shall he [Jesus, the Son of God] come forth unto me..." along with Matthew 2:6.

Consider also that in the LDS Journal of Discources Vol. 1 pp 50 - 51 Brigham Young said, "Jesus Christ was NOT begotten by the Holy Ghost."

Helaman 14:20-27 - "...a sign of his [Christ's] death, behold in that day that he shall suffer death the sun shall be darkened and refuse to give his light unto you; and also the moon and the stars; and there shall be no light upon the face of this land, even from the time that he shall suffer death, for the space of THREE DAYS, to the time that he shall rise again from the dead... and that darkness should cover the face of the whole earth for the space of THREE DAYS."

Cf. Matthew 27:45 - "Now from the sixth hour there was darkness over all the land unto the ninth hour." THREE HOURS, as likewise stated in Mark 15:33 & Luke 23:44.

Alma 46:13-15 - [In B.C. 73 he prayed] "for the blessings of liberty to rest upon his brethren, so long as there should a band of Christians remain to possess the land - For thus were all the true believers of Christ, who belonged to the church of God, called by those who did not belong to the church. And those who did belong to the church were faithful; yea, all those who were true believers in Christ took upon them, gladly, the name of Christ, or Christians as they were called, because of their belief in Christ who should come."

Cf. Acts 11:26 - [Circa A.D. 42] "And the disciples were called Christians first in Antioch."

2 Nephi ch. 2 gives the B of M account of Adam and Eve wherein it is claimed that they could have had no children unless they disobeyed God, "wherefore they would have remained in a state of innocence, having no joy, for they knew no misery; doing no good, for they knew no sin... Adam fell that men might be; and men are, that they might have joy."

Genesis gives a different account, for Adam and Eve were commanded to procreate prior to the matter of disobedience against God's command about one particular fruit-tree. However anyone 'reads' the Genesis account, it's clear that God would not have told them to procreate if eating the forbidden fruit was a euphemism for sex.

Those are just a few examples from the LDS Book of Mormon. There are many other LDS extra-biblical writings that clearly contradict the Bible, but when those are pointed out, LDS proponents are inclined to insist that such writings are indifferent. Some of us would disagree, but this is not the place for arguments!

Introduction: Joseph Fielding Smith, 10th president of the LDS Church, taught, "You cannot accept the books written by the authorities of the Church as standards in doctrine, only in so far as they accord with the revealed word in the standard works." The standard works are the Holy Bible, the Book of Mormon, Doctrine and Covenants, and the Pearl of Great Price. The Church does not accept the Journal of Discourses as a reliable expression of LDS Doctrine. On April 6, 1830, Joseph Smith organized The Church of Jesus Christ of Latter-day Saints and became its first president. He died on 27 June 1844. Accordingly, any writers before 1830 are disenfranchised.

Question: Do any of the LDS holy books (Book of Mormon, Doctrine & Covenants and Pearl of Great Price) ever clearly contradict the Bible?

Answer: There is only one major contradiction that matters. Joseph Smith claims that God was once a man. The LDS Church claims that the first spirit offspring of Elohim and his heavenly wife was Jehovah, who came to earth to be born as a human so he could progress to godhood. Mormons aspire to attaining godhood by working their way to the highest level of salvation. Mormon belief is based on these foundational doctrines.

Was God once a mortal, created man?

Joseph Smith: God An Exalted Man: “God himself was once as we are now, and is an exalted man, and sits enthroned in yonder heavens! That is the great secret. If the veil were rent today, and the great God who holds this world in its orbit, and who upholds all worlds and all things by His power, was to make himself visible,—I say, if you were to see him today, you would see him like a man in form—like yourselves in all the person, image, and very form as a man; for Adam was created in the very fashion, image and likeness of God, and received instruction from, and walked, talked and conversed with Him, as one man talks and communes with another... He was once a man like us; yea, that God himself, the Father of us all, dwelt on an earth, the same as Jesus Christ Himself did; and I will show it from the Bible.” [p. 305] Source: Official LDS website article on History of the Church and sermon by Joseph Smith: https://byustudies.byu.edu/content/volume-6-chapter-17

Mormons believe God has not always been the Supreme Being of the universe (Mormon Doctrine, p. 321) but attained that status through righteous living and persistent effort (Teachings of the Prophet Joseph Smith, p. 345). They believe God the Father has a “body of flesh and bones as tangible as man’s” (Doctrine and Covenants 130:22).

This is what the Bible says about God: There is only one true God (Deuteronomy 6:4; Isaiah 43:10; 44:6–8). He always has existed and always will exist (Deuteronomy 33:27; Psalm 90:2; 1 Timothy 1:17). He was not created but is the Creator (Genesis 1; Psalm 24:1; Isaiah 37:16). He is perfect, and no one else is equal to Him (Psalm 86:8; Isaiah 40:25). God the Father is not a man, nor was He ever (Numbers 23:19; 1 Samuel 15:29; Hosea 11:9). He is Spirit (John 4:24), and Spirit is not made of flesh and bone (Luke 24:39).

Is Jesus one of many other created spirit gods and can humans attain godhood?

Mormon leaders have taught that Jesus’ incarnation was the result of a physical relationship between God the Father and Mary (Journal of Discourses, vol. 8, p. 115; Mormon Doctrine, p. 547). Mormons believe Jesus is a god, but that any human can also become a god (Doctrine and Covenants 132:20; Teachings of the Prophet Joseph Smith, p. 345–354). Mormonism teaches that salvation can be earned by a combination of faith and good works (LDS Bible Dictionary, p. 697).

Contrary to this, Christians historically have taught that no one can achieve the status of God—only He is holy (1 Samuel 2:2). We can only be made holy in God’s sight through faith in Him (1 Corinthians 1:2). Jesus is the only begotten Son of God (John 3:16), is the only one ever to have lived a sinless life, and now has the highest place of honor in heaven (Hebrews 7:26). Jesus and God are one in essence, Jesus being the only man who existed before physical birth (John 1:1–8; 8:56). Jesus gave Himself to us as a sacrifice, God raised Him from the dead, and one day everyone will confess that Jesus Christ is Lord (Philippians 2:6–11). Jesus tells us it is impossible to get to heaven by our own works and that only by faith in Him is it possible (Matthew 19:26). We all deserve eternal punishment for our sins, but God’s infinite love and grace have allowed us a way out. “For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord” (Romans 6:23).

The ultimate goal of the Mormon gospel is to attain godhood (see McConkie, Mormon Doctrine 116-117; Book of Mormon [3 Nephi 27:13-21]; Doctrines of Salvation 1:268; 18:213; The 4th Article of Faith; Smith, Gospel Doctrine pg. 107; Brigham Young, Journal of Discourses 3:93; 3:247; 9:312; Gospel Principles 290; Doctrine and Covenants 39:5-6; 132:19-20). Mormons believe that there are different levels or kingdoms in the afterlife: the celestial kingdom, the terrestrial kingdom, the telestial kingdom, and outer darkness (Mormon Doctrine, p. 348). Where mankind will end up depends on what they believe and do in this life (2 Nephi 25:23; Articles of Faith, p.79).

In contrast, the Bible tells us that after death we go to heaven or hell based on whether or not we had faith in Jesus Christ as our Lord and Savior. To be absent from our bodies means, as believers, we are with the Lord (2 Corinthians 5:6–8). Unbelievers are sent to hell or the place of the dead (Luke 16:22–23). When Jesus comes the second time, we will receive resurrected, glorified bodies (1 Corinthians 15:50–54). There will be a new heaven and new earth for believers (Revelation 21:1), and unbelievers will be thrown into an everlasting lake of fire (Revelation 20:11–15). There is no second chance for redemption after death (Hebrews 9:27).

Source: https://www.gotquestions.org/Mormons.html

Edit: In response to the last comment, anything mentioned in the Articles of Faith can be considered foundational doctrine .