Sometimes this type of issue is best resolved by dropping the associated mission and getting it again from the contact.
To drop a mission you need to:
1) Leave the map that you are currently on & return to sector space.
2) Open your Episodes window (default "J")
3) Highlight the mission you wish to drop
4) Click the "drop" button located on the lower right hand corner of the window
5) Return to the contact that originally gave you the mission to get the mission again. Thank you for playing Star Trek Online.
Unfortunately the response I got is about as useful as Ice at the north pole.