Update (1/3/14): This bug has now been fixed. If you dock your blocks again and refresh your browser page, you should then still be able to use the new Edit menu.
We have identified a bug that is caused when you have blocks that are docked (like Navigation and Administration). Until we deploy a fix you will need to undock these blocks so that you are able to use the Edit menu to be able to edit activities and resources. Please see this link for more info. about how to undock a block. You will need to refresh your page or log-out of Moodle and back in after doing this before you can begin editing an item. This will not be an issue for you if you don't have any blocks docked. Please contact email@example.com if you have any questions. Thanks!