Studying Supreme Court clerks and how they function in chambers is a notoriously difficult enterprise. In the words of Mark Tushnet, himself a former clerk, "Clerks misrepresent what happens in the chambers of the justices for whom they work, while they don't know what happens inside the other chambers." In other words, they have a strong incentive to downplay their role, which makes it difficult to determine their impact on Supreme Court decision-making.
Still, there have been some valuable recent studies about Supreme Court clerks, and Adam Liptak has a very useful article summarizing the recent research. What most scholars agree on is that 1) clerks are increasingly tasked with writing large portions of judicial opinions, and 2) justices have become more likely to hire ideologically sympathetic clerks. Liptak's article evinces what I think is a perception among observers of the Court that neither of these developments is a good thing.
But I am much more sanguine. I don't deny the potential for principal-agent problems in which clerks abuse their discretion, but I suspect the potential is exaggerated, and the more important a case is, the less likely a clerk is to abuse his power. On the second point, it's unclear to what extent having judges ideologically screen clerks causes -- rather than simply reflects -- the increasing polarization of the Supreme Court. Even if we assume a causal relationship, this doesn't concern me for the simple reason that I think that the polarization of the Court is, on balance, a positive thing. People who prefer a Court in which the Chief Justice exerts more influence and produces more unanimous opinions are more likely to be troubled by the changing role of Supreme Court clerks.
-- Scott Lemieux