Distributed identity
Allow me to designate trusted friends / custodians. Store fractions of my private key with them, so that they can rebuild the key if I lost mine. They should also be able to issue a "revocation as of certain date" if my key is compromised, and vouch for my new key being a valid replacement of the old key. So my identity becomes "Bob Smith from Seattle, friend of Jane Doe from Portland and Sally X from Redmond". My social circle is my identity! Non-technical users will not even need to know what private key / public key is.
Relays
Introduce a notion of the "relay" server - a server where I will register my current IP address for direct p2p connection, or pick my "voicemail" if I can't be reach right away. I can have multiple relays. So my list of friends is a list of their public keys and their relays as best I know them. Whenever I publish new content, the software will aggressively push the data to each of my friends / subscribers. Each time my relay list is updated, it also gets pushed to everyone. If I can't find my friend's relay, I will query our mutual friends to see if they know where to find my lost friend.
Objects
There should be a way to create handles for real-life objects and locations. Since many people will end up creating different entries for the same object, there should be a way for me to record in my log that guid-a and guid-b refer to the same restaurant in my opinion. As well I could access similar opinion records made by my friends, or their friends.
Comments
Each post has an identity, as does each location. My friends can comment on those things in their own log, but I will only see these comments if I get to access those posts / locations myself (or I go out of my way to look for them). This way I know what my friends think of this article or this restaurant. Bye-bye Yelp, bye-bye fake Amazon reviews.
Content Curation
I will subscribe to certain bots / people who will tell me that some pieces of news floating around will be a waste of my time or be offensive. Bye-bye clickbait, bye-bye goatse.
Storage
Allow me to designate space to store my friend's encrypted blobs for them. They can back up their files to me, and I can backup to them.