According to the Florida Sun-Sentinal, part of the problem the Marlins had with the Rangers' offer for Beckett was that the Marlins had "off-field concerns" about Hank Blalock.
If "off-field", they mean, concerns about him hitting away from TBIA, then that makes sense. But otherwise, I have no idea what the "off-field concerns" would be, as I've heard nothing negative about Blalock off the field other than these two stories out of Florida from the past few days.