For example, I should be able to 'wait' for a team game but play something else in the meantime.

when enough people have expressed interest in that team game, then I should get notified (during whatever random game I'm playing) and we can all go play that team game

there should be some rules like you must join the game within 2 minutes of getting notified and you cannot leave in the middle. maybe you could even automatically connect the people.

basically there should be a system on Quake Live itself to let people group up for teamgames games where everyone starts & finishes the game together. you could even assign fair teams automatically to the best of your ability