Well, he wears clothes now and then, since he hasn't completely lost his sense for what human culture demands in order to concentrate on the real matters (instead of just starring at his blue dong). For example he wears a suit during the TV-interview and he also wore a speedo now and then when with other people (at least at the beginning, I think).
But it is also a fact and innate to the development of his character that he loses his connection to humanity and its puny problems more and more during the course of the story. This is indeed reflected in his growing reluctance to wear clothes, up until the point when he doesn't really care how people see him as he doesn't care about them anymore either (and neither to explain anything to them). It's not just about shame, but about cultural adaption and making your fellow people feel comfortable, for which Dr. Manhattan had absolutely no desire or reason anymore at the end.
(And from a filmmaker's perspective (beware I'm none) I'd say it also somehow shows the filmmakers' dedication to the source material. While it is really a bit irritating at first, since you don't expect that from a major Hollywood movie (and I found myself starring at his wang now and then in the cinema ;-)), it shows that the filmmakers don't take any consequences in transporting the story, no matter if it involves excessive violence or showing a blue penis, which for a more-or-less mainstream blockbuster is quite unusual.)