Author Existence Failure: Dante Alighieri is supposed to have died with the location of the final portions of Paradiso unknown. His ghost is said to have appeared to his son letting him know where the manuscript was. In a strangely related example, Dorothy L. Sayers died before completing her translation of The Divine Comedy; it was finished by Barbara Reynolds.
Dante referred to the poem simply as his "comedy." The title The Divine Comedy was not adopted until later.
Star Trek: The Next Generation said that Dante said something along the lines of "The hottest place in hell was reserved for good men who let evil happen." First, the center of hell is ice. Secondly, it's for traitors; people who are completely neutral aren't even allowed in hell, and their punishment is to go and be stuck between hell and purgatory, desiring any respite.
That might actually be the point. Good men who just weren't willing to commit themselves are in the bit of Hell furthest away from the ice. Thus, arguably, the bit that should be hottest.
Neon Genesis Evangelion fans are famous for their "four barons of hell" theory about the Evas' design. The most commonly cited source of this is the Inferno. There are no four barons of hell.
Extremely Lengthy Creation: The poem took over twelve years for Dante to compose, leaving him only a year on Earth left after writing an adventure set "midway through the journey of our life."
From Entertainment to Education: Originally meant to present an allegory on man's journey to God, the Comedy has universally been adopted as a teaching tool throughout Italian schools.
Half-Remembered Homage: Despite being one of the only characters mentioned in all three canticles, Ulysses is based entirely on the brief allusions to him in the work of Virgil without The Odyssey as a reference. In fact, Dante had never read The Odyssey in his whole life because that work was lost to Europe until a century after the Comedy was written.
Referenced by...: The comic book X-Men, alongside guest star Doctor Strange, once visited a hell modeled after the one in "Inferno", with the implication that Earth-616's version of Dante had really been to such a place.
In Purgatorio, we learn that the island of Purgatory is the only piece of land in antipodes (a.k.a. the Southern Hemisphere), surrounded by a huge ocean that covers one full hemisphere. To his credit, Dante always remembers that the sun would be to the north in the antipodes. (And remarkably enough, he describes a constellation of four bright stars that sounds suspiciously like the Southern Cross; he couldn't possibly have seen it, or even spoken to anyone who had. Critics generally think it's a metaphor for the Four Cardinal Virtues (fortitude, temperance, justice, and prudence) illuminating the life of the penitent sinner.)
Paradiso features a geocentric universe...sort of.
Averted in one noteworthy case: Inferno and Purgatorio clearly features a round Earth (proving that the idea that people once believed, especially during the Middle Ages, that the Earth was flat is completely wrong. The fact that the Earth is round is quite obvious to the senses and easily proven through basic geometry known since Antiquity).
Word of Dante: The Trope Namer is both the author of this work and the effect the work has had on people's perceptions of Hell. Despite the fact that the epic poem is not Biblical canon, and was never intended to be, a lot of what people think of when they imagine Hell comes from here. Most notably, the ideas of there being Circles of Hell.
Word of God: Some of Dante's thoughts and commentary on his work have survived the centuries, including one letter where he makes it clear that the Comedy serves as an Allegory for the relationship between freedom and salvation, among other ideas.
"The subject of the whole work, taken only from a literal standpoint, is simply the status of the soul after death, taken simply. The movement of the whole work turns from it and around it. If the work is taken allegorically, however, the subject is man, either gaining or losing merit through his freedom of will, subject to the justice of being rewarded or punished."
Write Who You Know: Dante populates the spirit world with his friends and enemies, alongside mythical and historical characters.
Despite being The Protagonist and the author, Dante's name is mentioned only once in the entire Comedy and it takes 64 cantos to get there.
Creator Backlash: There was a point where the Divine Comedy didn't play "Songs of Love" live because Hannon was sick of the association with Father Ted. "National Express" also saw a period of this.
Creator Killer: Although it wasn't a commercial failure, "National Express" did damage to Hannon's image among critics that his career never fully recovered from, because the perceived class snobbery of its lyrics (especially the bit about the hostess with "the arse [...] the size of a small country") finally gave people who'd always hated him for his upper-class background some ammunition.
Old Shame: Hannon was so unhappy with the group's first release Fanfare for the Comic Muse that he spent a long time pretending it didn't exist.