I have a real problem with the concept of anonymous peer review without editorial oversight or not included in a due peer review process. That said, I do recognize the interest for post-publication peer review due to lacks in the commonly used review processes, although I do not believe this should be allowed to be done anonymously.
Anonymous review is usual in the peer-review processes of most journals, but these comments are in general non-public or at least reviewed by an editor before publication. Some reviewers choose to do their peer-review work without the cover of anonymity and I encourage this. If you have constructive criticism on the work of an other and can this criticism is well founded, you can very well do it openly.
I believe that the best why to process with peer-review is with a two steps process, where first the submitted paper is published in an open discussion paper. Comments from the official reviewers are public and any one can comment on the papers. Following the peer review process, the paper is published in the official paper which may be with or without open access (I prefer those with open access). Such a process encourages quality and brings the whole community in the peer-review process, but under the oversight of editors.
Something like PubPeer is extremely tricky. It's an open door to abuse and for commenter to wash their dirty linen in public. I don't know if such a platform is a good idea, especially with anonymity. I'd rather have a good review of the peer-review processes commonly used.