Can Web of Trust/PGP be applied/adapted to client-server communication such as that handled by HTTP? Conceptually, HTTPS built on PGP? Would new products or services help the adoption of this (like a social network for PGP keys)?

Although it wouldn't solve all of the NSA techniques (social engineering, acquiring pre-encrypted data) it would certainly be harder to track down (i.e. steal, crack, coerce, subpoena, etc) tens of millions of keys rather than tens of thousands.