Share news items with only specific people (or only 1)
The one feature I miss from Reader than Old Reader doesn't have was the ability to share news items with a select audience via the use of shared folders converted to RSS feeds.
This was a bit of a hack, but it worked for my purpose: Sharing items only with my wife. Sure, someone could have found the feed and subscribed, but why would they care? It didn't consist of private news items, but it did consist of things my wife and I would talk about, and I didn't really want to share what I was reading/thinking about with everyone. Currently, since no one else follows me but my wife (and the opposite is true), it's no big deal for me to just use the normal share feature. If I were to have more friends sign up, I might not use the share feature in the same way.
An actual feature where users could specify who to share the item with (compare with sharing to anyone following you) would be neat. I suppose Google's answer to this is a Circle, but I refuse to sign up for Google+.
I imagine this could be like Google Reader's tag functionality, where you could just type someone's name and it would pop up in their feed list just like any other item.
Chris Swenson commented
This is similar, but not quite the same, as this item: