I actually never heard of Medium until I joined Steemit. So I decided to get set up over there.
I really like their onboarding process. They let you use Facebook to sign up, of course. But after that, they ask you to pick from a YUGE list of tags. I think Steemit should offer this feature as well. Your selection can be stored in json_metadata on the blockchain so that other clients can use it.
Another thing Medium does while onboarding is it offers you a list of people to follow. Steemit should do this as well.
Both of these ideas can be implemented without changing steemd but if we wanted to take it a step further, we could add some RPC methods to streamline things a bit. For instance, get_discussions_by_preferred_tags and get_discussions_by_feed_and_preferred_tags.
There are probably a bunch of other features Medium and LiveJournal have that are pretty much low-hanging fruit for Steemit to outright steal.
I'd like to see posts containing polls with participation happening on-chain. That could be done using custom_json operations, if we don't mind poll votes without incentive.