Glad to hear you are enjoying the book.
If it works on IE, then I'm not 100% sure that the fault lies with the service provider, although it's quite possible. My advice would be to jump ahead to chapter 6 - round page 162, and put some debugging alerts in, particular in the callback function getData and see what codes you are getting returned from Firefox. This won't hurt your understanding of the book.
Check that you are getting 200 from the status and 4 from the readystate and then go and query responseXML. If this is blank then try responseText. It could be that the server is returning the XML in a way that Firefox doesn't like, but it could be a problem with the setup, that IE is more tolerant of.
I sometimes wonder if the debug chapter shouldn't have been chapter 1, as Ajax apps while really useful can be quite finicky at times, and you've no idea how long I spent debugging some of the examples in the book. :-)