I think one of the models that would happily build stuff using an API would be role players. So some things that they'd need in applications, and I'm not sure how all of this translates into things the API needs:

Fast login switching
Something that tolerates network latency -- when I'm in the subway and I have no signal, I want to be able to hit send on an action and have the app realize that there's no connection and queue it for later, and in context with the fast login switching, if I'm working as User A and then as User B when the train comes out of the tunnel, I don't want my queued actions for User A to accidentally be sent as the current logged in user (B) instead.
Easy retrieval of related comments: given sufficient information to identify a comment, what is its direct parent, direct children, and whole thread? (Bonus points for easy pagination of the whole thread, because some RP threads get hella long.)
With any given comment, have I replied to it yet? And under which identity?


Some other things which are currently painful through the web involve entry management, like re-doing tags.

Retrieve all entries with a given tag.
Apply a given tag to an entry.
Retrieve the current tags for an entry.
Retrieve the current security settings for an entry. (Must play well with custom settings, including multiple custom security groups.)
Apply these security settings to an entry.
Retrieving the userpic for a given entry.
Retrieving the userpic for a given comment.


*pauses a bit to catch breath* I hope this is a good starting point.