The issue is that when the lobby starts the tab with the info is supposed to come down so that you can see the password and ip. If you are shift-tabbed ingame you need to have this tab come down to be able to connect, as the reconnect only brings up the server info. The only way for people to connect to servers now is to either get someone to give you the pw, or to alt-tab out of TF2 and join the lobby. If the lobby is already started then you can't join the lobby. You'll need to get it from someone which can be hard to do unless the leader is in mumble.
The suggestion to have a started lobbies tab would solve this, but it would be nice if the bug was just fixed.
I've been having this problem for a month or so now and I've seen other people with it as well.
-Tom