Today in order to see the option to display the advanced search criteria, you have to type something in the search box. The option should always be available to click on and expand that search dialogue. My users are constantly asking how to limit their search returns and once they find it, they depend on it more.
Additionally it would be great to be able to have the option top search on custom fields and to build and/or functionality. Today as an admin, I export everything and manage more easily is an external DB, anything more complex than a simple search, I reply on my external data for.