What it says on the tin. As it is we have to check manually after the first time if we switch back to the combat log.
It would allow an opponent to spam you and prevent viewing the combat log. Hate to have to acknowledge people might do that... but they might. Especially once the game is out of beta.
Which is a pity. I'd still like some easier way to follow the log AND follow the chat. Allowing a separate chat tag was supposed to improve things. I'm not sure what other good alternative there would be without crowding up the screen.
Simply having it acknowledge when there is new text and flash the header of the chat window (if you're on the combat log) would be enough.
Yep, submitted that to the codebase today. It was a feature missing in the initial chat UI redesign rollout. Once that code hits the live servers you should see that the Chat title bar changes to Chat (5), for example, when there are 5 unread chat messages. The title text also pulses visibly but (hopefully) not irritatingly whenever there are unread messages.