@DavidRoberts Since you are among users who are active in editing (at least a bit) I have added you to the list of the room owners.

It, for some reason, you do not wish to be among the room owners, feel free to remove yourself from the list.

Thanks! I don't know what that entails, but I guess I'll find out :-)

Actually, not really that much. An overview is given here: Is there a list of SE chat privileges, and the minimum reputation required for those privileges?

As a room owner, you can pin messages, move messages into another room. You can see content of a message even after it was deleted.

You can also edit feeds.

There are also some tools to deal with problematic users - but I have never used those.