I've been browsing the net and found theses two slides on site of XOM (XML object model):
Where they refer to SAX(push) and StAX(pull) parsers. So I'm wondering, what does it mean that a StAX parser isn't complete or correct in practice?
I believe the comment was aimed more generally at the pull-based XML APIs and parsers of the time, not just StAX and its implementations. At the time the slide deck was written (over ten years ago!), there were known deficiencies with XMLPULL API design regarding the handling of namespaces and ill-formed documents – in fact, it was Rusty Harold himself who reported them! Also, StAX was in its infancy (JSR 173 did not hit final release until 2004), and other implementations were apparently not yet considered mature.
Ten years is a long time in the software world, and things may well have changed in the intervening time. If you want to know what the current state of the art is for a particular parser or set of parsers, you should ask about it. See for example this much more recent exchange, and questions with the stax tag, on Stack Overflow.