"Completed On" Dates
 

Is there a way to set or change the date an item was completed when using OF for iPhone?

No, unless you want to set the date and time on the phone before launching OmniFocus and marking it complete. No guarantee that the likely out of order dates wouldn't give the sync code some indigestion! If you have a Mac, you can alter the completion date after the fact quite easily, although the last changed date on the action or project will reflect the time at which you made that change.

How badly do you need this, and how close does it have to be? If you're sufficiently determined and informed, you could edit the XML file(s) containing the database.