I don't think Peer Assessments work very well in a MOOC environment. For one thing, Peer Assessments are used when the work being assessed cannot be judged objectively, ie, like a multiple-choice answer that a computer program can correct. So all sorts of biases (sometimes real, sometimes imagined) creep in. The problem is compounded by course instructors trying to set up pseudo objective standards for grading, ie rate some aspect of the work on a 5 point scale where each scale has a short blurb explaining the meaning. If these standards are known in advance, people will build their work to conform to these objective standards and thereby "game" the system (sometimes forcing the peer to select one of these choices even though the work falls short in other areas that may be important).
The one place I have found Peer Assessments to work well (for the student but probably useless for marking purposes) was during the Social Network Analysis course on Coursera, where the final project was to use SNA for some real life project. People submitted their papers into the Coursera peer assessment system as normal and (I think) there was peer grading, but people also posted these links to the Discussion Forums. As a result, there was lots of conversations and a huge amount of learning that happened for all of us, as we got to see all (shared) projects not just the 3 or 4 assigned to each peer for review. The instructor Prof Lara Adamic was on the forums encouraging and offering suggestions for improvement.