Me and a friend found at least two missions that hang or bug out while in a team. We tried beaming up and down dropping and restarting the missions several times that had no effect.
1.The first one is from the cardassian arc (jabberwocky) While on mirror bajor after gul kardek first phase and cut scene and you need to defeat him a second time during phase two he's not there he doesn't spawn and cannot be found. But can be completed by playing the mission up to this point disbanding the team beaming up and continuing the mission while you will have to replay the first phase but is completable by all prior team members.
2. The second one is from the delta arc and called (what's left behind). When you get to the end of outpost 001 the elichi ground section at the final room and sela is supposed to enter the room she just stands there and you are unable to progress or finish the mission. Disbanding the team and continuing the mission will cause you to have to replay the entire outpost 001 elichi ground map but is completable by all prior team members.
I made another post earlier about the first one jabberwocky here (https://www.arcgames.com/en/forums/startrekonline#/discussion/1268073/mission-jabberwocky-broken-after-patch-unable-to-progress)
Before we discovered the second mission with a broken npc when players are in a team. I recommend moderators delete or merge that post with this one but please keep this one it's more detailed and focuses on the likely cause of the issue and has workaround information in it thank you.