While I am certainly among those inclined to applaud the Court's greater acceptance of empirical evidence, the Justices (and/or their clerks) simply have to know what they're doing. And in the empirical realm, sometimes they clearly do not.
The most recent example of this is highlighted by a piece (here) in today's NYT by Adam Liptak. If Liptak's reporting is accurate, Justice Kennedy’s majority opinion in Smith v. Doe (2003) includes a factual assertion about "the rate of recidivism [80%] of untreated offenders." Evidently, empirical support for the Court's factual assertion relies, at bottom, on a "1986 article in Psychology Today." One consequence, as Liptak observes, is that "the basis for much of American jurisprudence and legislation about sex offenders was rooted in an offhand and unsupported statement in a mass-market magazine, not a peer-reviewed journal."