Changing the favicon because of such a small issue sounds silly to me. If you need to be notified of new inbox messages, consider the next Stackapps:
- stacknotify google chrome extensionstacknotify google chrome extension
- A user script to update the page/tab title with # of unread notificationsA user script to update the page/tab title with # of unread notifications
If you want to, I can create a userscript that colors the whole bar red on new inbox messages.