BlackBerry 7 allowed me to flag an email (still works on BlackBerry 10), but also to change the flag to a check mark. This would sync from my desktop to my BlackBerry and vice versa. This feature appears to have been lost in BlackBerry 10. If so, died BlackBerry intend to bring it back in future upgrades?
You would not be able to set a date from the messages, once you flag a message, the flagged messages would appear on the Flagged Messages section of the "Remember" app in which you can set a due date.....Hope this answers the question. Please try this and let know.
Mine isn't synced (yet) so I can't test that part. But you're right about part of it. The option exists to clear the flag, but not specifically to check it off as complete. Could have sworn it was there, but I don't see that option anywhere now either.