I am trying to do a Character Battle Tournament, similar to what GameFAQs does, but with teams rather than single characters. However, everytime I try to do a COM vs. COM battle, it wont let me start a game unless I am playing as one of the teams. Is there a way to do all COM battles, or can it be put in a future update?

You can't, at the moment. This feature hasn't been requested much because, well, watching the AI fight against the AI isn't exactly a sight to behold. You could have an "arbiter" human team with one worm that stays out of harm's way or surrenders/suicides on the first turn.

I was able to launch a PC vs. PC battle in WWP.

However after the round ended, it immediately skipped to the next round, and the game never ended.

Lol.
Well, by all means, CyberShadow's idea is the best. But wouldn't that mean that the game would end?
But how anyone would want to see A.I. killing each-other is beyond my belief.

Well, by all means, CyberShadow's idea is the best. But wouldn't that mean that the game would end?
I tried (v3.6.29.0) with one human team and two AI teams and the game didn't end when I surrendered.
But how anyone would want to see A.I. killing each-other is beyond my belief.
Well, the official WA screensaver does exactly that, without any human teams though.

Speaking of the screensaver:
CyberShadow, could you re-release a WA screensaver with the high resolution/widescreen support?

Nevermind.
http://forum.team17.co.uk/showthread.php?t=30525
Doesn't work with recent replays anymore though.
Update, Bloopy?