A WebmasterWorld thread has a very interesting questions. Does Google, or any other search engine, associate link popularity to a portion of a page? For example, if I link to a page and anchor down to a specific portion of that page, would Google see that portion to be more important than the other portions?
Anchor Link, I use them all the time to link to specific posts, is defined here.
My thoughts are that Google and other engines do not point specific popularity to a specific portion of a page. It would be interesting if they did and how that would work exactly.
Forum discussion at WebmasterWorld, but the topic is not exactly about that - more focused towards penalties on specific portions of pages.