Currently, [[Special:ProtectedPages]] gives the option to choose semi and full levels for edit-protections or move-protections. But it doesn't allow to list pages that are semi-edit-protected and fully-move-protected, or fully-edit-protected and semi-move-protected.
It would be useful to have those options for maintenance (e.g., to make sure no pages are in the second case) and certain analysis purposes.
So the move and edit permissions should be separated, the interface could be changed to something like Namespace:[all, (article), ...] Edit restriction level: [none,semi,full] Move restriction level:[none,semi,full]. Default would be none, so it wouldn't show any page initially, and couldn't show pages to semi or full levels in the same time, which hasn't much interest anyway.