Several authors are mentioned in the book of Proverbs: Solomon (1:1; 10:1; 25:11), Hezekiah (25:1), Agur (30:1), and Lemuel (31:1). None of these authors was without sin.(Rom. 3:23). So, your question has much broader implications: why should we listen to any author of Scripture?

We do not rely on Scripture because of the perfect life, thoughts, or deeds of its authors. We rely on Scripture because it is inspired by the Holy Spirit:

2 Timothy 3:16 All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness.

2 Peter 1:20-21 Above all, you must understand that no prophecy of Scripture came about by the prophet's own interpretation of things. For prophecy never had its origin in the human will, but prophets, though human, spoke from God as they were carried along by the Holy Spirit.

As one may see, the Author of Scripture is the Holy Spirit. However, God can use any means to communicate his truth - even a donkey (Num. 22:21-41; 2 Pet. 2:15-16), a stone (Luke 19:39-40), or other authors (lower case "a"). It is only by the grace of God that human authors were used to communicate God's revelation.

Solomon asked God for the ability to judge Israel and to "discern between good and evil" (1 Kings 3:9). Solomon's wisdom is in the Bible because God supernaturally communicated it to him to govern his people (1 Kings 3:3-15). Therefore, like others, he was a mouthpiece through whom God communicated his word, imperfect though he was.

Since this is the word of Almighty God, not only should we listen to it, we should take heed to it (Ps. 119). It is life-changing. It is alive. Romans 13:13 convicted Augustine. For Martin Luther it was Romans 1:17. For Jonathan Edwards it was 1 Timothy 1:17.

The first instance, that I remember, of that sort of inward, sweet delight in God and divine things, that I have lived much in since, was on reading these words, 1 Tim. 1:17, "Now unto the King eternal, immortal, invisible, the only wise God, be honor and glory for ever and ever. Amen." As I read the words, there came into my soul ... a sense of the glory of the Divine Being; a new sense quite different from anything I ever experienced before. Never any words of Scripture seemed to me as these words did. (Works of Jonathan Edwards, vol. 1, p. 12).

Scripture is transforming when we read it, study it, devour it, meditate upon it, and the Holy Spirit applies it. Though God used men to scribe it, it is really from God. Yes, men spoke and wrote it, but it was God-breathed. It is the living word of God (1 Pet. 1:23). Though the authors' personalities and writing styles are seen in the texts, God is sill the author. What the Bible authors wrote was not merely from their own limited point of view; rather it was by God's revelation. The Bible authors were not the origin of the truths. They were simply the means, the agents, the channels by which it was communicated. The Bible is God's Bible. The Word is God's word. The truth is God's truth. Its revelation is God's revelation. Its meaning is God's meaning. These authors were carried along by the Holy Spirit. Scripture was not left to mere human ability or will. The Holy Spirit himself carried the process to completion.

God's Flawless Word
Inspiration and Accuracy
Inerrancy and Canonicity