I would like to be able to drag and drop files, selections, etc. on to the Places menu. While hovering, the Places menu would open, revealing the Desktop and Home folder entries, the Bookmarks sub-menu, and the Recent Documents sub-menus. I could then move over the Bookmarks sub-menu, hover over say 'Documents', and a file browser would pop open. Now I can drop my file directly in it.

Another useful drop target would be the Recent Files entries. I could select some text in a browser window, drag 'n drop to the Places menu, hover over a recently opened text document and it would open up in gedit. Now I can drop the text directly onto the text doc.

This would be somewhat analogous to something which already does work:

You can currently drag over to the task bar and hover over an app button. The application pops to the front. So if you already have a file browser opened at the correct place then you're all set.  Otherwise, it would be nice to be able to drop to the Places menu.

A refinement might be that you could drop directly onto a bookmarked folder in the Places menu without first hovering and waiting for a file browser window to pop up. In this case, the file would be copied in the background and the menu would snap shut -- a very convenient way to quickly organise files into different folders without opening lots of windows.