I am using Oneiric Beta(fresh install), and the Thunderbird install seems to have an issue. When I receive a new mail in the only account configured(my college webmail, IMAP over LAN), there is a system notification, but the messaging menu does not show any unread mail count, the envelope does not turn blue, and the launcher icon does not show any unread mails either. Thunderbird works perfectly fine, but the notify-osd bubble is the only notification of the mail. In short, the whole Ubuntu Integration add-on seems to be not working, although it is enabled. I have tried purging and resetting Thunderbird a few times, but the icon stubbornly remains white. The Messaging Menu is working, because I have used chat as well as gm-notify, and they are working fine. Only Thunderbird isn't working.
Give that Oneiric is only 1 day away, I think we can consider this a genuine issue.