Saved Searches for Calendar, Story Budget and other Management screens
We only save one state right now. The idea is to remember the user's last state, but also allow them to save various sets of filters, ones that they would use frequently, to allow easy switching.
E.g. I'm going to set up saved filters: "Posts by me that are Pensing Review" and "News Posts Ready for Publish".
Seems to make a lot of sense, but it also duplicates the trusty old browser functionality that is the bookmark. If you're looking for the simplest possible implementation, you could display a button with a link that people can drag into their bookmarks bar, and that button would point to the calendar / budget that was active at the time when they dragged the button. Basically bookmarklets.