There is just one function that I have not seen in the apps I have tried (outside a hosted app like LiveJournal) that would be highly valuable to me: The option to make any post "private" so that only logged in authors could read it.
I think this would be a very popular feature. The nature of weblogging is such that many times an author would like to record something for his/her own benefit, but not share it with the public. Or perhaps he/she is willing to share it only with other members of that weblog.
Ideally, I believe, there would be three levels of privacy available on each post: 1) Public (viewable by any visitor), 2) Members Only (viewable by all members of that weblog) and 3) private (viewable only by the author of the post).
I hope that these ideas will be considered for incorporation in the near future. The addition of this feature would distinguish Serendipity even more from most other weblogging applications which are currently available.
Best of luck to you as you continue to develop this application.