So one nice thing about living in Chicago is that I'm now just a train (or taxi) ride away from the Central Division meetings of the American Philosophical Association. I was thus able to attend an unusually substantive session of the North American Nietzsche Society with presentations by Richard Schacht (emeritus, Illinois) and Maudemarie Clark (UC Riverside). Schacht argued forcefully that we need to acknowledge the influence of Lamarck's view that acquired characteristics are heritable on many aspects of Nietzsche's thought, while Clark presented a careful challenge to Schacht's reading of particular bits of textual evidence for his thesis. I expect (though this isn't certain) that the papers will appear in a forthcoming issue of International Studies in Philosophy.
My own view, which I offered in discussion, is something of a middle ground between Schacht and Clark (though perhaps closer to Schacht's view of the matter). Schacht is right to emphasize that it really would be astonishing if Nietzsche--self-educated, as he was, in matters scientific--dissented from the familiar Lamarckian orthodoxy of the era. So we should expect to find some passages in his corpus that just presuppose, as uncontroversial, Lamarckian assumptions.
On the other hand, it did seem to me that Schacht swept far too many passages, including large parts of the Genealogy, into the Lamarckian framework, without adequate evidence. As Clark pointed out, many passages Schacht invoked seemed equally compatible with the idea of cultural (rather than biological) transmission of acquired characteristics. Some of the passages (BGE 264 most strikingly) were ambiguous as between the claim that personality traits are heritable (which we know now to be true: cf. discussion in Knobe & Leiter ) and the distinctively Lamarckian claim that acquired characteristics can be inherited. (There is, to be sure, no reason to think Nietzsche was sensitive to this distinction [between heritability and inheritance], but here at least there's a way to interpret what Nietzsche says in a way that does not make it dependent on a manifestly false view, i.e., the Lamarckian one.) Finally, many of the phenomenona in question--such as the acquisition of bad conscience--seem clearly explicable on the assumption not that acquired characteristics were inherited, but rather that certain kinds of recurrent social stimuli reproduce the same kind of effect across generations. So, e.g., if bad conscience represents the internalization of cruelty in response to the constraints that civilization place on human beings, then we should expect bad consicence to be a recurrent attribute of creatures like us brought up within those contraints. The only 'biological' assumption here is that humans all have some degree of instrinctive cruelty; but insofar as other aspects of their biology drive them towards civilized forms of social intercourse with their fellows, we should expect 'bad conscience' to arise across generations.