I don't know if anyone else has this problem on FED side, but I have a mission that just wont clear agter numerous attempts. Halting the Gorn Advance just can't get it to clear, not the "Daily" mission, the first one that gives 1980 skill points, and 1650 expertise with the main reward of a choice of kits. It doesn't say anything about minerals like the "daily" does so I don't know if it's bugged or what.
I've had the same issue. I've run the fleet action multiple times, and have dropped the mission, picked it back up, and tried again, but it will not complete for me either. Not sure if this is related to the issue with the daily, but I believe the map was updated, so it's possible that some unlisted objective isn't being fulfilled any longer by the current version.
it appears that no one knows the answer, or just doesn't care..it's only a small problem so it gets little attention when they have so many "bigger" prob's to work on (like, small mocha cappachino, or the double chocolate latte)
More than likely it's tied to the old version of the FA, not the new 5-man one. Thus when you complete the new one, it doesn't actually register as having completed since it's looking for a completion update from the 20-man version.