The no-doubt biggest concern with Granderson is his awful platoon split. Over the course of his career (619 AB), Granderson has put up a horrid line of .210/.270/.344 against lefties. Versus righties, he's hit to a much more attractive .292/.367/.528 line. These numbers scream platoon player, and many have suggested signing someone who mashes lefties to compensate for Granderson's weakness.
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Analyzing the New York Yankees’ Most Recent Addition, Curtis Granderson
I discussed right after the trade went down, the Yankees have acquired Curtis Granderson from the Tigers. Granderson's past few seasons have been very interesting. He peaked in 2007 with a 7.4(!) WAR season and has since regressed to seasons of 3.8 and 3.4 WAR in '08 and '09, respectively.