Why does Google report such a small subset of a page's backlinks?
 

The weird thing is that the "Show pages that contain the term http://www.example.com" option actually shows more backlinks than the "Show pages that link to http://www.example.com" option.

AFAIK Google only shows links from PR4+ sites. There are sites dedicated to link popularity that should display more results.

That's right, and in addition to that, a search for "Show pages that contain the term http://www.example.com" brings up pages have the link to you, even if there wasn't a backlink update (PR update) in the meantime.