What are the advantages and disadvantages of making the review content public?
I believe that there are many sides to this, but overall I think that the "sanctity" of blind review should be maintained. In either case, I think that at most, one can allow access to the review content, but not reveal the identities of the reviewers, nor the review scores. 

While it is true that one can sometimes guess a reviewer's identity from the content of the reviews, I think that this is not an issue because


It's still a guess, and more importantly
If your review potentially reveals your identity (say by you unnecessarily suggesting all of your papers as ones that should be cited), then it's a bad review, and the practice should be discouraged. 


Review scores are often useful to weed out clear accepts and clear rejects, but become really hazy when talking about borderline cases (see further comments below).

Having gotten that out of the way - 

Pros of publishing reviews:


It encourages more careful reviews: if I know that my reviews will be public I'm encouraged to make sure that they're more careful.
It discourages abusive and unprofessional language in reviews. Ad hominem attacks in reviews do happen, and are a bad practice.
It encourages editors/program chairs to select reviewers who do a good job. I've seen reviewers submitting a single paragraph; this is not ok.


Cons of publishing reviews:


It encourages reviewers hold back and not write scathing/overly gushing reviews even if they truly feel strongly about the paper.
It may render papers less readable, as authors would rely on the reviews to clarify what they should have (as Buffy mentions) 
Reviewers will worry about their identity being compromised, and thus early career researchers may not want to review at all/write very positive reviews.
It may cause community dissent: interdisciplinary communities host several small sub-communities, each with its own publication norms and acceptance thresholds. This is already a major issue, that will be further exacerbated by revealing reviews (this may be a pro, not entirely decided!). 


I think that one of the main reasons I'm against revealing reviews is because the review process, unfortunately, involves a lot of random luck. As the NIPS experiment shows, PCs can widely disagree on a lot of papers. It is important to note that there is general agreement on what are very bad papers and very good papers, but a significant chunk of them are borderline cases that could swing either way. I think that showing the reviews for borderline cases might be a bad idea, as it would cause a lot of dissent in the community ("why did my paper, with one weak reject, one weak accept and one accept, got rejected but my paper with better scores got accepted?"). I think that the "clear accept" papers can be easily listed with their reviews; the others? Not so sure...

Overall, I think that presenting reviews might be good in some cases and should involve the informed consent of both the authors and all reviewers. However, I worry about it becoming a norm. Paraphrasing a bit, review decisions are like sausages: it's better not to see how they're made.