I navigated to the search by clicking the advert in the SO sidebar, and found myself here:

http://careers.stackoverflow.com/jobs?campaign=PrettyFooter

I entered some parameters, the address changed to : http://careers.stackoverflow.com/jobs?campaign=PrettyFooter#/?searchTerm=Grails&location=Manchester&range=40 but the results didn't change.

I edited the address to http://careers.stackoverflow.com/jobs?searchTerm=Grails&location=Manchester&range=40 and loaded into a new tab. The results loaded appropriately.

I modified my search criteria and clicked search again, the address changed to http://careers.stackoverflow.com/jobs?searchTerm=Grails&location=Manchester&range=40#/?searchTerm=Java&location=Manchester&range=40 But still no change in results.

TL;DR: The search button logic is broken in Firefox 4.0.2 on Windows XP.