In my opinion Spectating matches would be a great addition to tf2center as it would be great for newer players to understand how matches are run and listen in to mumble - as you can do this already. A good way to police this would be to make sure you can't start spectating after a lobby has started but you can spectate if you are listed as a 'Spectator' as the lobby is starting up. I know there are many streamers and youtube videos that would give new players insight but i feel that spectating a live game would give a better feel of tf2.
Argontrax