If you reload your browser a lot, or you have two people trying to edit the same page on top of each other, sometimes there's this super weird state where you're "kinda" in edit mode. The page has the dotted lines, but nothing highlights when you roll over it. The tool bar looks like it thinks you're editing the page, but the exit edit mode button isn't active. Super-duper annoying.
If this happens to you, as it just did to me, there's two tricks you can use:
Go get a beer/coffee. Every 20 minutes or so locked out pages get automatically turned back in. If your schedule allows, this is the best solution for your well being.
Edit Properties. I was still able to bring up the Properties dialog and when I hit save (after making no changes) everything was back to normal.