It is none the less a tremendous literary achievement - to merge Judeo-Christian and classical mythologies, and recent (for 1300) European history, into a fairly seamless world; to construct mappable spaces of Hell, Purgatory and Heaven; and to come out of all this with a reasoned but impassioned emphasis on Love as the driving force behind God and the universe - all these are remarkable things.
I can see why Inferno is the most popular of the three - evil is always more interesting than good or repentance. Oddly enough, though, the one moment when the narrative really grabbed me was towards the end of Purgatorio, when Virgil hands over the role of guide to Beatrice. I don't know if this is a general finding, or something to do with the translation, or just the mood I was in at the time.
Anyway, I now have a good sense of the overall shape of the story, and will look out for an edition which gives me more explanation of the details.