I’ve been using the excellent push notifications plugin for a while and would like to see the underlying desktop notifications extended and simplified to make it even more useful.
Apparently you only get notifications of new posts and not likes. I find it unnecessarily confusing that there are two different different notifications systems. It would be much simpler for all the site notifications to create a desktop (and push) notifications as well. Even better if you could choose the type of notifications you want.
Also, it would be great to get notifications for admin stuff like flags and moderation queue. The current implementation of wait at least an hour (usually longer) until you get an email feels very slow when I could get instant push notification instead.