Value of Print on Demand Publishing of PhD Dissertation
I am wondering that if a PhD dissertation is of sufficient standard to be passed by the relevant university (assuming the University is reputable itself), why does it need to be peer-reviewed?


In an ideal world, that could be reasonable, but in practice it's unclear what the standards are for a dissertation.  For example, imagine a student who works diligently for years but doesn't accomplish much.  Many advisors, even in very prestigious departments, will eventually let the student graduate with a minimal dissertation.  Or what about a sloppy student whose dissertation is full of minor errors? Hopefully the advisor will put pressure on the student to fix the errors, but sometimes, given the choice between letting the student graduate and keeping on struggling fruitlessly with this, the advisor caves in and approves a shoddy thesis.  Perhaps this shouldn't happen, but occasionally it does.

Of course peer-reviewed journals are also far from perfect, but their judgments are somewhat clearer.  A paper accepted by the Transactions of the American Mathematical Society is a more meaningful guarantee of quality than a dissertation from a top-five math department, although on average the dissertations will be better.

Peer review can also lead to valuable feedback and suggestions.  A dissertation has often not received many comments from anyone not on the thesis committee, and getting anonymous feedback from other experts can be important.


  Also, if it is reproduced as a book by POD, why shouldn't it add to the publication record of the author.


The problem is that it doesn't "add" anything that wasn't already there.  Your dissertation is part of your academic track record, and your decision to let a company print it on demand is not additional evidence of quality or impact.

It's certainly useful to try to get visibility for your dissertation.  In a field where this is considered appropriate, posting it online (for example, on the arXiv) is very valuable.  Far more people will look at it there than via any POD publisher.  Letting someone print it on demand too can't hurt, as long as there are no copyright issues, but it won't help much either.


  The PhD is often the first major work of many students (I fall in this category) so making the most out of it is the only way to add value to one's CV. 


Certainly.  In most fields, you can make the most of it academically by turning it into journal articles or a scholarly book.  Mathematics isn't a book-based field, so I can't speak to this from personal experience, but my understanding is that publishing a dissertation as a book involves a lot of review and editing, and it's really not the same as letting a POD publisher reprint the dissertation.