I've typed up notes from a very information-rich one-on-one session with Roan Kattouw, author of much of MediaWiki's API code, on how to write an extension that provides custom API calls and uses Ajax to invoke them:
http://lalashan.mcmaster.ca/theobio/worden/index.php/Wikipedia_SF_Hackat...

It might be useful to integrate some of this into the official documentation on mediawiki.org. For right now I've just dumped it into my wiki.

(Please forgive the hashtag in the title - it's to get it onto the twitter hashstream for the workshop so that people who want to see it will see it)