If I may suggest something.
The push notifications are a killer feature to me, I think for many other users as well. What would be really great is you could implement an easy to use notification management feature within the app. So you can check all activities one by one and mark them as read for yourself and give you the options to react to that specific activity.
Also, when we get mentioned a nice notifications pops up but if we get mentioned in a new post there is no quick way of getting to that post if I'm correct. I would have to remember who mentioned me, go to their blog and find the post.
@good-karma perhaps these are already on your roadmap, perhaps they're not... hope it helps though.
Thank you! Yes, Notification center/page is on todo list :)