Is there a programmatic way to purge a specific cache item. I have a no-so-frequent need to purge the caches for activity completion (for various reasons that would probably horrify the core team, but we won't speak of that) or can someone point me to the code where caching of this value occurs so I can figure out how to do it myself.
Sounds like you're looking for cache_helper::purge_by_definition($component, $area)
You can do this under Admin -> Plugins -> Caching -> Cache configuration. There is a separate purge link for each bit of cache.