My second question is - what thematic purpose does Dr. Manhattan serve?
He's an incredibly interesting character, no doubt - creative concept, and implemented wonderfully. But he's so far removed from human thinking that it's hard to relate him to the human condition, and he also has very little effect on the story.
One of the first layers of Watchmen that I was able to pick at was the "Superhero Genre Deconstruction" layer. In it, Manhattan, whose original analog was the Charlton Comics superhero Captain Atom, fills in for the superman (little "s"). If you're going to write a twelve-issue commentary on the state of the comics industry, you've got to include a Superman (big "S") analog, yeah? Just like you've got to have the crazed vigilante who sees everything in black and white, the technological vigilante detective (two sides of the Batman coin), and, of course, the under-written and almost story-deficient female hero (which is commentary on the fact that female characters have notoriously gotten short shrift, story-wise, in the roughly seventy year history of the genre).
Thinking causally, what effects can we realistically expect a super-powered being to have on our world? To the politically cynical Moore, it certainly makes sense that he would be used as a militaristic deterrent, all the while attempting to serve mankind by mass-producing polyacetylene batteries so as to give us electric cars and provide us with a cleaner atmosphere, which is certainly commenting on the state of science in the twentieth century, as well.
"Moore's a fucking genius."
And, yes, I realize that I almost certainly used the word "causally" wrong, but, really, fuck you.