Thanks for the great plugin!
I encountered a problem, which is not really severe but confusing. In the chat window there is an option to log out (why actually?). After clicking it, I'm asked whether I want to log out from WordPress. If I confirm, a full WordPress screen appears inside the chat frame (probably mistaking it for the whole browser window).
I run version 22.214.171.124 of the BuddyPress Chat Component and the above described happened when I was logged in as admin.