As an alternative to this suggestion to enhance the ability to track feature requests, and thus the development of the SO platform, I'd like to suggest another alternative.
Rather than bookmarking searches externally, allow us to construct searches based on tags and keywords and store them for later use. These searches could acts as personalized filters that would be available just to the person who constructed it. A further extension could make these searches available to others as a "popular" search. These could be provided to the user by replacing the current search box with a combo box in which the dropdown is only available if the user has saved a particular search.
Searches could be saved either by using an interface to explicitly construct one or by clicking a "Add to Saved Searches" button (a plus icon next to the searches box?) that would take the current url, parse it for search terms to construct the saved search, and allow you to give it a friendly name. The interface for building searches could be extended to list the most popular searches (by construction and use) isolated from actual user data. These could simply be invoked from the page or added to the user's personal store.