<p>Is there something special about Safari for Windows and AJAX?<br>
In other words: Are there some common pitfalls I should keep in mind?</p>

Safari is really standards compliant.  Unless you're using some really esoteric browser features, in general if something works in Firefox, I've found it works without modification in Windows Safari.
Apple has
a developer center for web developers
, but I didn't find anything too useful there.