There are rumors aplenty that Columbia and NYU may move to something like the Yale system of essentially two grades--Honors/Pass--now that Harvard and Stanford are going that route (though perhaps these two will actually utilize Low Pass and Fail, unlike Yale). NYU, given its size, can probably least afford to eliminate sorting mechanisms, especially since it appears Columbia grads are still slightly preferred by the very top NYC firms. For those who have asked, I think there is essentially no chance Chicago will go this route, or anything like this route.
From the standpoint of the students, an actual grading system has one very substantial benefit: it rewards your actual performance in law school rather than your ability to schmooze up professors or your undergraduate pedigree--since, bear in mind, that law firms, elite government jobs, and judges will all still be looking for ways to evaluate applicants. And if they can't see actual law school grades, they are going to fall back on other factors that may have little to do with what you accomplish in law school.
UPDATE: A law professor at a top school writes:
I think the last point in your post about eliminating grades was right on. At least when I was there, the grading system at Yale did not really lessen the sense of competitiveness, at least for those whose ambitions were higher than landing a job at a top firm. It simply displaced the competition towards sucking up to the professors whom students perceived to be able to deliver the goods (esp. clerkships). For those of us who wanted to clerk but did not really want to participate in that game, the lack of grades was actually fairly frustrating. I also think there are some pernicious distributive consequences to the sucking-up system, since (although my only evidence for this is anecdotal) I think minority students tend to be particularly reluctant to engage in it.