Update: Burp Suite Pro 1.4.10 supports JSON scanning out of the box, see http://releases.portswigger.net/2012/06/v1410.html
A while ago Alex came up with a solution to get Burp to scan JSON formatted requests. It required a rather involved setup with two Burp listeners and an Apache server acting as a proxy packing and unpacking JSON data for Burp's consumption.