If we aim for mass adoption, good user experience is absolutely essential. The first users might be forgiving but this period will end quickly. Here are my suggestions listed in order of importance.
Critical flaws
(a) No search utility
We are still relying on Google search which is very inaccurate. Also, currently there is no way to find a user by their name, unless you know the exact spelling and then type it as an URL.
(b) Spam/abuse flag is misused
Spam/abuse flagging a critical part of every posting/blogging website, yet we don't have it working properly: it's being misused on a massive scale, either by trolls (which should be outvoted but there is no way to do it) or genuine users who, due to not having an alternative option, use it to express their intent of lowering the payout. A solution has been suggested here.
(c) Chaos in tags/topics
We have a real mess in this area. It's hard to come up with a robust solution but still we could alleviate the situation by offering some hints about tags/topics that already exist. Also, the sort order of the tags/topics list should be more predictable - the current ordering is a mystery to me.
Important improvements
(a) Latest replies/comments
Replies/comments are currently hidden behind posts. It would be cool to see a live flow of new replies/comments on the front page, in real-time as they are generated. This way we could promote replies/comments and at the same time encourage users to read and upvote the parent posts.
(b) My portfolio
As suggested by @ash : let the user decide which of his/her own posts should be displayed on the profile page. It would allow us to use Steemit as a real blogging platform.
(c) My bookmarks
Let the users collect other people's posts which they consider valuable or just want to keep track of them for future reference. Personally, I've lost track of many valuable posts and now have no idea how to find them.
Nice to have
(a) Integrated storage for images
We should stop relying on external URLs for images.
(b) Mobile support
Some of the functionality does not work well on smaller screens (e.g. videos don't fit on mobile screens).
(c) Notifications
As suggested by @juanlibertad : it would be nice to have notifications for replies, upvotes, etc. It should be an opt-in feature.