I had this same issue with one of my missions. The Patrol the Risa Sector mission had the white check, but I couldn't complete it. It said to talk to Sulu so I went to ESD and talked to him, but he didn't have any option to complete the mission. I submitted a ticket, but ended up dropping the quest since I had completed half of it before Season 5 went live and the other half after; I figured maybe that screwed something up. But I can't re-take it now that I dropped it so.