While Twitter's official Windows Phone 7 client lacks notifications about received direct messages or mentions, Beezz - an emerging Twitter client which is available from the Windows Phone 7 Marketplace for a couple of weeks now - is expected to become the first Twitter app to support push notifications. In its next update, Beezz is expected to support Live Tiles as well as toast notifications for direct messages and mentions. While Twitter itself has also announced to support sooner or later push notifications (without mentioning Live Tiles or toast notifications so we can only guess what Twitter is planning), the missing notifications of Twitter (as well as Facebook) is a major drawback for Windows Phone 7.
According to the developer, the Beezz update ran through Microsoft's Marketplace certification process already and should be available anytime later today or tomorrow. So far, Beezz for Windows Phone 7 was offered free of charge; no word yet if this will change with the feature-enhanced version.
Cheers ~ Arne