I think the next 'reddit' needs to be an evolution and innovative in some ways. Cracking the comment thread organization would be a good place to start, that seems like something that could really be improved on. Also, as a few other people have mentioned in here, decentralizing/decoupling the central 'brand' from the individual 'sub sites' seems important from both a technical and business standpoint.
I am working on a feedly alternative that also ingests the voting/ranking of other sites like Reddit and Hacker News.
Do you think implementing discussions that can be integrated via Javascipt a la disqus would be a good solution? Building voting/raking ingestion and also discussion ingestion could also be done via an Open Protocol so all Feedreader could benefit.