This morning the Hardball Times published a fabulous piece of research by Bojan Koprivica on catchers blocking pitches.
Bojan's work builds on the knowledge established by previous research on the topic by Dan Turkenkopf and Dave Allen. There is a lot of meat to chew on Bojan's article, but I highly recommend taking the time to digest it if catcher fielding is a topic that interests you.
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So, ironically, the running game is probably one of the least-well understood parts of catcher fielding at the moment.
Beyond that, pitch calling is probably the hardest part of catcher fielding to quantify at the moment, and I don't hold out any hoping of cracking that one in the immediate future.