The corner pickers 'resticking' when hidden/shown may be a bug, I'll pass it along for someone to look into. You can tear it off and then switch to docking mode and the corner pickers will remain visible (this may also be a bug, but I like it so I'm not reporting it >.> ).

You can switch to full screen mode from Docking Mode - press 'tab' to clear the screen of everything except the guides shortcuts and any open floating menus.