Possible team level drop when mission completes

If a team is running a mission that isn't the leader's and the needed objective(s) is completed, then the team's level immediately goes to whatever the level of the leader is. If a team is running a level 40 mission, completes it, and the star holder is level 20, the team drops to level 20. If said team is still fighting, then you can see where this is an issue. Add in the bug where team members don't show up correctly and an easy fix is to pass the star, and now you can see an even bigger issue. People pass star, mission completes, team level drops.

Can the level drop happen while you're still inside a mission? I've never seen that happen.

Yep. It's been a rather recent bug, but it's happened a couple of times.