The groups system just needs to be thrown out and redone from scratch >_>. It has so many problems and bugs that it's almost unusable. You mentioned some things like not being able to search for groups at all, and how it uses the old forum format and looks ugly. There are also a lot of bugs caused by using the old unsupported forum format too.
I think it would be nice if you could search for groups, and also see what is inside a group before joining. Maybe groups could also allow public posting in certain threads for people who aren't a member, and also allow anyone to see the member list too. Also the limit for joining groups should be raised slightly / removed.
Of course none of this will ever happen unless Simon comes back ): (and even then it won't happen lol)
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I don't like "who is online?" counters very much but I guess I would be ok with one. #powder is also linked to in game and on the wiki, i'm not sure if having a more obvious link to it would be a good idea.
I tried asking him about that once, he never replied :P
Also I thought of another idea, it should show new posts from groups you are in in the "Recent Topics" section at the bottom of the forums maybe. And / or have a "subforum" with all the threads from your groups. And everything would be clearly marked with links to the actual group. This way people would see group activity easier and be a bigger part of it. It's annoying to check for new posts in all of your groups right now.
The groups system is usable but doesn't look good compared to the rest of the website. @jacksonmj's user script does fix a majority of the problems and makes it look better. Details on how to install it here.