I got a master's degree (humanities) at a state university where the average SAT score for accepted freshmen is 915. There were several graduates of the university in the program, and, frankly, they were among the worst students in the cohort--and when I say "worst," I mean really, really bad.

That said, the professors were good and had gotten their PhDs from well regarded institutions. I was able to do what I needed to do to challenge myself, and I really got a lot out of the program. The grade inflation was horrific though, with people graduating with honors who really shouldn't have been graduating at all. What this means if you are the sort of student who thinks you are getting a good education just because you are getting an A, you would be mistaken.

This might be an extreme case though. I don't know how different a Harvard education would be from, say, a University of Michigan education in terms of what is offered in the way of things like problem sets.