It would be great if you could bookmark the results of a search.
The obvious solution of making searches a GET request rather than a POST won't work. This is because non-ASCII characters can't be reliably included in a URL, breaking searching for many of our users.
The proper way to implement this is to store searches in Confluence with an identifier. The permalink for a search is then simply a link to repeat the saved search.
This is part of the Smart Lists feature, which incorporates other improvements to searching.