The screenplay could've only be written by Greene, really, it contains exactly the same sardonic defeatism of many of his great works, from
Our Man in Havana to
the Quiet American. The opening voiceover ("I never knew Vienna before the war...") is classic Greene, really, as is, I think the attention to detail in terms of the setting and the fact Lime is so alluring. The actual novella is far less satisfying than Greene's screenplay, something he admitted himself. There's less ambiguity and it changes around key details (in particular the ending) that make the film so perfectly black. Bear in mind that Greene actually worked (breifly) as a spy at one stage.
Regarding whether there's any religious implications in either the title or the story, well, I don't think it's a naked allegory, like say, Greene's
The Power and the Glory (to say nothing of
the End of the Affair!), but Greene always loved the contradictions inherent in Catholocism: Namely, though God judges your worldly sins, only God can judge what a wordly sin
is. Much like Harry Lime, Greene used this 'loophole' as an excuse for all sorts of disreputable behaviour!
The Third Man Argument is also the name for an incredibly obtuse piece of philosophy about how we group things together. But I doubt it'd have anything to do with that.
As for the film, I wouldn't remove a single frame of it- I think it's perfect. There's the great offhand humour that permeates a lot of the scenes, like the running joke to do with Cotten's character and his inability to pronounce the police inspector's name correctly, or the fact that Lime is quite literally out of the picture until nearly two-thirds of the way into it, or
that zither score. Moreover, there's that final scene, apparently something of an accident. Carol Reed accidentally held onto the shot for a good second longer than he intended, but as a result, you see the girl walking off and Cotten standing there, aimlessly flicking his ciggarrette onto the ground. I find that sequence oddly moving, actually. Anyway, here's
Roger Ebert's excellent short essay on the film.
It's before my time but I've been told, he never came back from Karangahape Road.