I'm being CO in 50-member clan and sometimes it's super hard to communicate with other leaders and keep track on everything that happens when we are international clan and have CO's, Elders an members around the world. What I really would want is some separated specific log for clan events.
A new window for list, who kicked whom out and the kick message, who joined when and when someone left, who started war search, who demoted or promoted someone and so one... Every clan related notification - all that notifications that are currently send to clan chat. In my opinion it's not right place for it since the chat can only save 100 last messages. We have really chatty clan and if I'm more than 2-3 hours away I can miss a lot of things.
And this is mostly for that I can't be online 24/7 but I would really like to know what has happen in that time I was not around. Sure, I can ask people, but it usually takes unnecessary time to do that, when the right peoples are not online at the same time that much...
So, I think I would not be that big a change (in developers side) since the game already has the notifications, only new tab next to 'inbox' where they would go and it could save up like every message from past 2 weeks or something.
But it would really make a difference for moderating a clan and help everyone to keep track of what has happened in clan.