Is there a way to edit the Logged Time entries for other Users using an Administrator's account/permissions? 

Sometimes we find a user will log time to the wrong project, or we wish to log the time for that user.

Hi John, not at the moment but there's a Feature Request for this: OP-2326 (I upvoted for you).
A (not very pretty) workaround would be to log unit costs named after your colleagues.