How sound is the doctrine in Dante's Inferno? I have read Dante's Inferno and was wondering how Theologically sound some of the points-of-view really are?
Now I know Dante's Inferno was not written by a priest or anyone really involved in any sort of real church. So it could be that it was never really meant to be considered as anything but a flight-of-fancy,but still the religious imagery is so vivid and profound that I cannot seem to shake the idea that these where the cherished beliefs of the writer.
What shook me is the idea that the well-meaning pagan would go to hell. This struck me as an odd belief when the Bible mentions that those who don't have the law are still governed by it, their conscience bearing witness.
This seems to me to be at odds with what the Bible teaches. I guess Dante did not believe in the salvation of infants either.
The second issue that struck me is how bad the sin of suicide is considered in this book.  Now we know suicide is often a result of very real mental disease.
The idea that these people would be denied entry into heaven as a matter of principle over a disease they may not have any control over, does not strike me as the actions of an all-good and loving God.
Now again this work may very well not be endorsed by any church, but still the theological implications may be worth discussing as there exist the real chance that some may people reading may consider it doctrine.
How sound is the doctrine in Dante's Inferno?
Dante’s Inferno is basically just one part of the now famous work known as The Divine Comedy. Dante Alighieri’s epic poem was written in 1321 and was written as a literary work and not a theological work. We have to keep that in mind.
Dante was quite orthodox for his time place in history.
As a literary work, it was intended to be a poem which included the use of allegory, symbolism,  philosophy, and theology, as understood in his times.

Dante’s three-part epic poem the Divine Comedy, or Commedia, is one of the most influential and dense works of poetic literature in the Western tradition.  Building off Homer and Virgil, and influencing the likes of Chaucer, Milton, Blake, and Tennyson, as well as bringing to popular consciousness and form the modern Italian language, Dante’s epic delves into the meaning of allegory, poetry, love, truth, and philosophy.  Dante’s poetry rests on the classical presumptions of the human being: earthly love does have Divine, or transcendent, character and quality.  Moreover, following from the Christian tradition which Dante is part of and extols, it is first the love of things temporal when finally, and properly ordered, allows one to enjoy earthly loves while proceeding to move toward the permanent things: the good, true, and beautiful.
Admittedly, the poem is exceedingly dense and is ripe with all types of layers of allegory, philosophy, and theology. For a basic understanding of the intellectual content of the poem, I cannot go too deep into the themes for risk of losing you, the reader.  As such, I will explore a few of the major themes in the various books – starting with Inferno – and give explanation and context to these.
Understanding the Inferno: The Construction of Hell
To understand Dante’s construction of Hell we must first understand some basic things about Christian theology.  In Christian theology, God is understood as Love and Truth. This is important to know when exploring the nine circles of Hell, and especially the separation between the first four five circles with the final four circles.  Furthermore, Christian anthropology asserts that man has a telos and that this telos is to live a life in union with truth, wisdom, and love. Without knowing Truth, which is impossible with reason or wisdom, then one cannot properly love.  Without this one cannot live a truly fulfilled and happy life which is what all humans seek. - Dante’s Inferno: Understanding Hell

Dante’s Divine Comedy is a poem containing a  mixture of the Biblical truths, Roman Catholicism, mythology, and medieval traditions.

The poem is written in the first person as Dante describes his imaginative journey through the three realms of the dead: Inferno (hell); Purgatorio (Purgatory); and Paradiso (heaven).
The philosophy of the poem is a mixture of the Bible, Roman Catholicism, mythology, and medieval tradition. Where Dante draws on his knowledge of the Bible, the poem is truthful and insightful. Where he draws on the other sources, the poem departs from truth.
One extra-biblical source Dante drew upon was Islamic tradition (Hadiths) as depicted in Muhammed’s “Night Journey.” According to one scholar, Islamic eschatology has exercised “an extraordinary influence on Chinese and Christian thought. Among numerous popular eschatological works written by Christians, Dante’s Divina Commedia is an example of Islamic influence” (Islam by Solomon Nigosian, Crucible, 1987, page 152).
In fairness to Dante, however, it should be noted that his work is intended to be literary, not theological. It does reflect a deep yearning to understand the mysteries of life and death and, as such, has generated tremendous interest over the centuries, remaining extremely popular even today. - Is The Divine Comedy / Dante’s Inferno a biblically accurate description of heaven and hell?

Not completely backed up biblically or even by any tradition, Dante places Satan frozen in the middle of a lake of ice. He even places Christ’s betrayer Judas in his mouth as if eating souls like a ravenous lion. In his three mouths, he chews on Judas Iscariot, Marcus Junius Brutus, and Gaius Cassius Longinus. The Divine Comedy runs like a medieval novel than a theological work.

Be alert and of sober mind. Your enemy the devil prowls around like a roaring lion looking for someone to devour. - 1 Peter 5:8

His epic poem does deviate from biblical sources and traditional pius beliefs, but his imagery, at least to me remains awesome!

Satan is trapped in the frozen central zone in the Ninth Circle of Hell, Inferno, Canto 34. Illustration by Gustave Doré.
The following may be of some interest:

Why is the Devil also known as Lucifer (and other names) three-faced? Symbolic meaning of Dante in his Canto XXXIV of the Divine Comedy.