How do I know who is talking?

Solution 1:

On the mission launch screen, there is a little speaker icon by each players name... it is red if they have no mic, blue if they do have one. When someone is talking it is blue with sound waves coming off of it. Get them talking before the mission launches, mute them there and you should be good to go!

Solution 2:

I had the same problem. After a few hours I found this post: http://forum.ea.com/eaforum/posts/list/7577844.page

Make a party and invite no one.

This post was written while the game was in beta, but I didn't find any other useful solution. IMO, the "back-button solution" is kind of annoying.