1) Tell me what my friends HAVEN'T seen yet
Various user research I've done suggests there's a sharing stigma around being last to the party - sharing something with a bunch of friends only to hear back "yeah saw that two days ago." Given this, I believe there's potential value in prompting me to share - generally or directed to certain people - with the call to action "Hey,
The mechanics of doing this are actually not that difficult if you have access as a first or third party to G+, Twitter or Facebook graphs. Here's one way it could work:
I'm reading an article on a tech blog and click +1 to share it to my G+ circles. In the publish confirmation box, I get suggested friends to add specifically to the share, based on (i) Google's knowledge of their interests & (ii) Google knowing that they haven't seen this URL yet via search/email/reader/G+/etc.
2) Which of my friends was FIRST to see it
Anyone who isn't a n00b knows what FIRST! means but yet none of these social sharing systems do a very good job of rewarding the initial curator. Who was the first of my friends to watch the video that later went viral? Which person I follow was first to tweet out the link to that amazing blog post? Who listened to that cool band before they went big time?
The ability to identify curators as trendspotters is pretty valuable generally and to be known among your friends as the one who got there early, major clout (if not Klout).
Again, not that hard to do within a closed system. Twitter could certainly do this - for a given link I share or see, who was the first of the people I follow to tweet it, or I could pivot to see who were the first people to tweet it overall (you'd run into the self-promotion issue there as the author is likely the first to tweet, but perhaps still valuable).