Same deal here - There's 12 other threads on this topic with others having the same issue.

Emptying my inventory did nothing for me...I had plenty of inventory slots available at turn in to Commander Swift. Even after completing Darkhold AND my Immortal Flames hunting log, I still can not request a promotion because the guys still tells me that I have to complete a trial (Darkhold) as well as my level 2 hunting log - (completed). I am level 49 by the way and have completed the main story quest as far as I can to this point (escape from CC).

No green explanation point over Swifts head anymore, and he won't talk to me other than to tell me that there's work to be done.

All I care to do is request a promotion with my Grand Company. I could care less whether or not there is an item/monetary reward for completing Darkhold...I just want Swift to recognize that I've done both.

Any assistance would be appreciated.