In The Leagueof Extraordinary Gentlemen: The Black Dossier, a section written in a pastiche of Shakespeare, we learn that the original 007 was, of all people, Prospero. At first I thought this connection was a bit far fetched. It wasn't until later that I learned a bit about John Dee's career. Moore has Prospero stand in for Dee in the League universe. Dee, best known as an occultist, was also a spymaster for Elizabeth. He corresponded with the Court in secret, signing his name with a special glyph of his own invention: two circles under the top line of an acute angle.◊ And yes, it was this practice that inspired Ian Fleming during the creation of the James Bond character. I'll never doubt Moore's research again. Also, it's widely thought that Shakespeare based Prospero on John Dee, adding another layer to the symbolism.
The Black Dossier reveals the significance of Dr. No's name- a tip off that there was No Doctor. But one thing Moore didn't point out- in the novel, No is killed by being crushed by a pile of guano, an indicator that the Dr. No story was, in fact, a load of crap.
In 1910, there is a reference to Ice-9, which suggests that the events of Cat's Cradle happened in the League-verse. However, in that novel, a bit of Ice-9 falls into the ocean and destroys the world by freezing the world's oceans, events that are obviously difficult to reconcile with League continuity. Fridge Brilliance hits when you remember that superheroes are also real in this universe, and if they're anywhere near as powerful as they are in their own comics, the oceans freezing over doesn't seem like an insurmountable problem after all—they deal with stuff like that all the time.
Heck, there may be an even simpler answer. Setting the events of the play in 1910 instead of Victoria's crowning, having the Earl of Gurney show up six decades early, Jack the Ripper... the entire set up is hugely anachronistic. Just like the actual Threepenny Opera is!
Crowley, 60's rock, and Harry Potter. All are treated Satanically in Century. This seems an odd move for the left-hand path follower Alan Moore. Until you remember that people still falsely accused these things of being Satanic, and all fiction is true in this continuity.