When this feature was first announced I was fairly against it as I found the notifications to be kind of obnoxious. I waited a few days now to give myself a chance to warm up to the feature. Heck I've even clicked on a bunch of the items to try in an attempt to see the feature in a new light. Unfortunately my opinion of the notifications has not improved.
I still find them to be annoying. They pop up pretty frequently and most of the time I dismiss them before even reading what it says. Now maybe this is just an issue with me personally. I tend to turn push notifications off on just about every single application I get on my phone, which get's me to my central problem with this system.
It's not tailored to my interests at all. If I could set up my own feed to let me know when new SSIS questions or answers come up that would be something I would be interested in. Instead right now it's just any activity that's done by high rep users. No offence to Rolando but no matter how brilliant his answer/comment may be I don't care about MySQL. Even if the answer or comment is of my interest the notification does not show that. Let's say Aaron has some comment that I would be interested in reading the notification does not have any synopsis to tease me into clicking on it. I would need to click on every comment/answer that happens every day to assure that I'm seeing comments of interest.
That's just my two cents. I'm all for the concept but having a hard time finding use for this in it's current state.