Have two different chat boxes instead of one (split the current one down the middle of the screen into a left and right half) for team games with one box being only team comments, and the other being for everyone. For example, any posts made in the right chat box will be seen by team members only, and any posts made in the left will be seen by everyone.
This will improve the following aspects of the site:
Opposing teams will talk to each other more
You do not have to uncheck that little box
No more of those bold "[team]" in front of posts
Team chats will not get cluttered up by chat visible to all
Chat will not be 99% team chat, making the visible parts lost to all view
All the higher ranked players that have a million random people comment in their games every 2 seconds will be able to take advantage of the game chat more easily (must get annoying)