Are you aware of any compatibility quirks and look-out-for's between the XmlHttpRequest implementations of IE, Firefox, Opera and Safari (other than the constructor)? Does your book cover this topic?
Except for Opera -- which I think has only added support recently -- I've tested my Ajax apps on all those browsers and aside from the IE-vs-others means of creating the object (ActiveX vs native object), I haven't really run into any major compatibility issues. Not that I've nessecarily plumbed the depths of all the capabilities -- but I have given it a pretty good shakedown.