Minor spoilers follow.
The reason the film is appearing in this blog is that there were a couple of Classics/Ancient History references. First and most obviously, Anton, the herald into Parnassus' world, presented himself as Mercury, the messenger of the gods (Greek Hermes). So far, so obvious! Mercury was a very busy god, being in charge of commerce, taking messages and taking the sould of the dead from the upper to the lower world, among other things. Whether he's here in his messenger capacity, or here to show souls to the lower world, probably depends on how you read the film (or which bit of the film you're watching). I suspect the transportation of souls bit is the most relevant.
Less obviously, Tony, the new arrival among the troupe, owns a small pipe which he is particularly attached to. This reminded me very much of Pan, the god who gives his name to Pan pipes, and the mysterious pipe seems at times to have some special quality. Tony certainly seems to ascribe a magical quality to the pipes (though perhaps mistakenly).
A strange 'gondola' appears a couple of times in the film, but although the dialogue gives it the Venetian name, the boat itself, and more especially its environment, owe more to Egypt. At one point, we see the boat floating along in front of a huge black pyramid. At one end of the boat is a carved head of Anubis, one of the Egyptian gods of the dead (there are several Egyptian gods associated with death and the underworld). Anubis was the jackal-headed god of embalming and took care of people in the transition from death to rebirth in the afterlife - rather like Mercury. He is particularly prominent during a touching speech about famous people who died young (which I can't help thinking might have been a late addition to the script).
Anubis, statuette from the Ptolemaic period, Metropolitan Museum of Art
As I said, I really enjoyed the film, but I have to confess, I'm not quite clear on exactly what happened at the end, though I think I followed it. A second viewing would probably clear it up a bit! The film is deliberately reminiscent of Alice in Wonderland, which it actually quotes at one point. It also had sequences that reminded me of the Terry Jones-scripted Jim Henson film Labyrinth, though that might just be because Labyrinth is also influenced by Alice in Wonderland. The ending (if I understood it right) reminded me of the Star Trek: Voyager episode 'The Thaw', which is quite possibly the freakiest, scariest episode of Star Trek I've ever seen, but also unusually thoughtful and ahead of its time (it predates The Matrix, which shares some concepts with it). The film is also very funny, which is great to see - Anton's drag costume at one point made me expect him to start yelling 'spam, spam, spam, spam, spam!' The costumes are absolutely gorgeous! I love the Imaginarium itself, with its wonderful Victorian feel (I was surprised to see that the film is actually set in the here and now!) and elaborate sets, and Tony's updated version is rather good too. The performances are brilliant all round - Johnny Depp and the late Heath Ledger are predictably brilliant, but Ledger's tragic death halfway through filming shouldn't be allowed to overshadow Lily Cole and Andrew Garfield as Parnassus' daughter and protege, who are also excellent, and Christopher Plummer, who is reliably great as well. The film is definitely worth a look, and I appreciated more than I've appreciated some other Gilliam stuff, though the ending doesn't quite match the pace and bizarre but understandable logic of the rest of it.