What evidence and authority make The Song of Solomon a work of spiritual inspiration and not an erotic poem?

This is a sort of rebuttal to what has been written thus far in answer to the question. The love described in the Song of Songs is centered on the physical attractiveness and erotic appeal of the people involved. (Observe the rapturous influence of this "sister" and "bride" on the groom, for instance.) The spiritual love between God and his people does not flow from any attractiveness of people, external or otherwise, but from God's nature to pity and love the unlovable and restore his marred image to us. "For man looks at the outward appearance, but Yahweh looks at the heart,” God tells us in 1 Samuel 16:7 (World English Bible). The hearts of people are not attractive to God: "The heart is deceitful above all things and it is exceedingly corrupt. Who can know it?" (Jeremiah 17:9, World English Bible). Neither is our love for God based on his irresistible attractiveness to us but on the power of his Holy Spirit that shows us his relentless love. So, God loves unlovable humanity; and we by the power of his Spirit are drawn to him despite our natural aversion to him. Quite a different kind of love than that described in Song of Songs.

It takes a lot of imagination to make the erotic themes of Song of Songs into an allegory of what has transpired between God and mankind, whether mankind is represented by Israel in right standing with God or the church in relation to Christ. Our loving relationship with God is that of spiritual communion, empowered by the Holy Spirit--not mutual attraction based partly on endearing qualities in us, but a supernatural connection by his power and Spirit. It is no surprise that the themes of this writing are not captured in the New Testament, and the Song of Songs is not quoted anywhere there, even though the image of bride and bridegroom is employed in the New Testament.

The Song of Songs was a part of the Septuagint, a Greek translation of the Old Testament finished at least 135 years BC, hence before the Christian era.

"Early in the Christian era" - No, all the books of the Old Testament were accepted and received into the canon of Scripture by the Jews. Christians merely took as Old Testament Scripture what the Jews had already determined. So it was received before the Christian era, and was not decided by Christians.

The Song of Solomon is an expression of romantic love. It can be understood as a celebration of the love between a man and a woman in engagement, betrothal and marriage. But it cannot be only about human love because it is called "The Song of Songs": the Holy Spirit would not give such a title to a work which was only about human love. It is an allegory, and poetic allegories are not in the habit of explaining themselves, by which much of their poetic beauty would be lost.

The Song is also to be understood as an expression of the love God has for his people. God expressly says in the Old Testament through Isaiah

"For your Maker is your husband: the LORD of hosts is his name, and your redeemer the Holy One of Israel. The God of the whole earth shall he be called." Isaiah 54:5

The Song of Solomon is a fuller expression of this verse of Isaiah.

In the Old Testament God is the husband of the people of God, the Jews/Israelites. In the New Testament our Lord Jesus Christ is the bridegroom of his people, the Church (John 3:29).

In truth the whole history of the Universe can be regarded as the ultimate romance: Christ wants to pour out his love upon his chosen bride; chosen bride rebels and plays the harlot; bride now fears her destiny; Christ woos her back by the ultimate act of loving, passionate, self-sacrifice; bride is won back; Christ at last pours out his love and brings his bride to perfection; they live happily ever after.. "And I John saw the holy city, the new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband" (Rev 21:2).

Just as Adam was put into a deep sleep and suffered the loss of a rib in order to gain a bride, so Jesus also suffered and died and rose again to gain his Bride.

The woman was made of a rib out of the side of Adam; not made out of his head to rule over him, nor out of his feet to be trampled upon by him, but out of his side to be equal with him, under his arm to be protected, and near his heart to be beloved. (Matthew Henry)

Furthermore, the Song is not to be understood as merely an allegory of the mutual love between Christ and the whole body of the Church. Rather, it is to be seen as an allegory of the mutual love between Christ and each individual believer:

Taking, therefore, this Song as an allegory, whose imagery has been drawn from the court of Solomon, for illustrating the mutual love of Christ and the Church, we cannot understand it fully, without viewing that love as exercised in the case of individual believers. Taking the Church as a whole, its love becomes a generality of the vaguest kind, intangible and unsatisfactory. But when we take the exercises of an individual heart, all is intelligible and interesting. Jesus loves the Church, by loving every single member of the Church; and manifests his love to the Church, by a special manifestation made to every member of the Church.. "Sees all, as if that all were one, Loves one, as if that one were all." (George Burrowes, Commentary on The Song of Solomon, 1853, Geneva Series, page 85).

When our Lord spoke to the woman of Samaria in John 4 he said

If you knew the gift of God and who it is that says to you "Give me a drink" then you would have asked of him and he would have given you living water". (John 4:10)

and again he said

whosoever drinks the water that I shall give him shall never thirst: but the water that I shall give him shall be in him a well of water springing up into everlasting life. (John 4:14)

He is speaking of the gift of the Holy Spirit that he shall give to all who believe on him. But it is noteworthy that the only place in the Old Testament that speaks of "a well of living waters" is in the Song of Solomon:

a garden enclosed is my sister, my spouse, a spring shut up, a fountain sealed..a fountain of gardens, a well of living waters, and streams from Lebanon. (Song 4:12..15)

Jesus is proposing to the woman of Samaria. If she believes on him she shall become his bride and he shall become her bridegroom. Is he not also confirming the Song of Solomon to be a spiritual work of the love the Saviour has for his Bride, the Church, and every individual member of it?

The woman of Samaria had six men in her life, five husbands and one who was not her husband. When she believed on him, Jesus became her seventh, perfect husband.

The Song of Songs, which is Solomon's, is clearly an expression of what inspired the very creation of masculinity and femininity.

It is the mystery of Christ and the Church.

No, it is not 'incoherent'. There is a structure to the book and a development in the narrative. The book is educated, informative, sensitive and moving.

Yes, it is inspired. The full meaning of the book is revealed in the New Testament scriptures and in the Book of Revelation which parallels the concepts of Christ and the Church seen, in prophetic imagery, in the Song of Songs.

There is nothing lewd or indiscriminate about the love being expressed. It is nuptial, not licentious. It is about a marriage, not an affair. It is about a lifelong bond of union that wishes it had always been so.

Unto the pure, all things are pure, Titus 1:15.

Ten years ago, I put the entire book into English verse so that it may be read as poetry and parts may be sung in worship.

This may be freely downloaded from my website. It is part of the book 'The Songs of the Witnesses'