One of the problems is you are not likely to get truly honest feedback. That opens things up to dispute, and that puts the interviewer in an awkward position: if they cannot articulate a point properly, even if valid, the interviewee is left feeling they should have "passed". In the worst case, they could claim the interviewer was prejudiced against them and file a labor dispute or lawsuit.
It's also often highly subjective, for example:
"I don't think you demonstrated the depth of knowledge in (technology x) we're looking for in this position"
"Well I've developed several applications that work, so clearly I do know it"
What you can do along the way is ask questions like "Would you like me to elaborate on that?" or "did I answer your question adequately?" if you get the sense you may not have. For code, the list on the page is actually decent - ask up front about the assumptions, how much you should focus on defensive coding, etc.
Also I have found that when asking for feedback, it can lead to interesting discussions which might make the interviewer change his/her mind.
This of course is personal preference...