Node permissions - administer content
I now understand how this works:

If you want a user to be able to edit all content types, regardless, you are supposed to use "Bypass Content Access Types".

"Administer Content" allows people without "Bypass Content Access Types" access to the Author and Promotion panels on the rhside of the node edit screen. i.e. they can change the Author (UID) and the creation date/time, and can either promote the content to the homepage or make it sticky. 

"Administer Content" also gives access to the Revisions tab for all content types - but those permissions are duplicated - a user may already have them if type-specific revision permissions have been set, e.g:


Basic page: Delete revisions
Basic page: Revert revisions


(Note: Administer Content used to be called Administer Nodes and the latter name is still used internally.)