Paul's PieSpy tries to figure out which people are talking to each other on a set of IRC channels in order to guess social relationships. I think a more interesting problem would be to figure out what people are talking about, so you could track memes as they propagate from person to person, and produce live displays of the most-talked-about subjects.
The simplest way to look at memes would be to track URLs that people have referred to; this is easy, but doesn't produce particularly interesting data (particularly for a small network). A more complex approach would do some very basic language analysis to watch for repeated concepts, perhaps using some external data (Google searches?) to group related phrases.
The easiest way to listen to all communications on an IRC network would be to intercept or implement the inter-server or services protocols. You'd need to be careful not to reveal data from private channels, though.
The Daily Chump Bot cheats: it produces blog-like output by getting people to explicitly tag their statements to indicate what topic they're talking about. Cooperation between several of these could provide interesting cross-channel communication.