Make sure you have set the right button to the appropriate setting in the mighty mouse system preferences pane. The default is for the right click to be the same as the left click (primary click) so you have to change it yourself.
What is the right button set as in System Preferences/Mouse? My wireless Mighty Mouse has it set to "Secondary Button", and works fine in OS X and Win98se, and in Fedora as well. I can't believe XP is different from 98se.
I think AlanH has the right answer, you have to make sure that the right button is set up properly in system preferences. My Mighty Mouse (corded) works just fine (both left and right button clicks) in both XP and Vista.