What are my duties regarding reporting plagiarism when reviewing a fellow graduate student's paper? I am a PhD student, and have just finished the last part of my course requirement. My last assignment is to review several other student's term projects from a seminar course.

One of the projects I have been asked to review is rife with plagiarism. More than 75% of the paper is plagiarized, from over two dozen different sources, including academic papers, stackoverflow.com, and wikipedia. I have reported all of this to my professor, along with a detailed summary of which parts are taken from where.

However, some of the paper appears to be plagiarized from the student's own earlier assignments, in a different course. It's fairly obvious that this is the case because they first plagiarized the assignment description to summarize the problem they wanted to study, and then provide an answer to said problem, including answering discussion questions that are on the assignment, but somewhat unrelated to their main topic.

I know the professor who taught the earlier course well. Should I contact him directly? Should I suggest to my current instructor that the earlier professor be notified as well? Which course of action is more appropriate?
If you've spotted plagiarism, you have a duty to report it to a responsible authority. Just because the student is a fellow graduate student in your department does not absolve you of the duty. However, the politics of the situation can make things much more complicated, because it may lead to intra-departmental conflict, which is most certainly not a good thing.

I would believe the correct initial approach is to notify the professor of the current course of the current and past plagiarism. If you feel that no appropriate action has been taken, then you can consider notifying the instructor of the past course; however, the actions that can probably be taken are somewhat more limited than for a class where the final grades have not yet been assigned or have only recently posted.

How far you want to pursue this matter, on the other hand, depends on how serious you believe the transgression is. If the plagiarism is serious enough that it calls into doubt the student's ability to be an independent researcher, then further escalation—perhaps (in order of approach) to the graduate "officer" for the department, the chair of the department, or the dean for graduate students—may be necessary, if your initial efforts don't lead anywhere. This is, admittedly, a rather severe course of action, and one which may cause problems for you later down the road. So I would also recommend talking to your advisor as well, and solicit feedback as to what are the consequences of pursuing this.