IHE has the latest details. The right-wing Volokh blog, whose selective interest in these issues is well-known, suggests this violates the professor's academic freedom. That seems to me dubious, except on a very capacious conception of academic freedom in which anything an academic says is part of that freedom, a conception which has no legal status. Professor McAdams's research profile does not suggest that his blogging critical of a colleague's teaching practices had anything to do with his scholarship, and so academic freedom is not at issue. On the other hand, he is clearly being punished for his speech, and while Marquette, as a private employer, is not bound by constitutional standards, it should honor a moral commitment to freedom of speech. As the IHE article notes, McAdams's suspension also does seem very suspect from the standpoint of AAUP guidelines. The strongest argument that could be made in favor of the university's action, at least on the facts that are public, is that by inciting a right-wing firestorm about the philosophy instructor's teaching, Professor McAdams interfered with university functions, though I'm not sure how persuasive I find that argument. (Consistent with the New Infantilism now running rampant in the blogosphere, some people suggested that because the philosophy instructor was a graduate student, though one running her own class, and McAdams a faculty member in a different department, he had some kind of special pedagogical or other obligation not to criticize her. That argument has no merit as a matter of law or AAUP norms.)
UPDATE: Over at IHE, there is a strong statement in the comments from longtime academic freedom commentator John K. Wilson (one of the few who was consistently on the right side of the Ward Churchill debacle):
I haven't studied the case enough to make a judgment on whether the TA was right or wrong (or both). But I know with certainty that Marquette is wrong to suspend a professor for talking about the case and expressing an opinion. McAdams is perfectly free to publicly criticize a TA's approach, and nothing about it constitutes harassment or some violation of privacy. The fact that the university can't even clarify exactly why they're suspending McAdams is particularly suspect. McAdams' blog should not be grounds for any kind of investigation; the fact that he was suspended without a hearing shows that this punishment is entirely illegitimate.
That last point is particularly important: suspension without even a hearing indicates that Marquette has just left the AAUP universe. What a disgrace.
ANOTHER: Justin Weinberg (South Carolina) offers a rather tendentious characterization of McAdams's offenses in the third update, and even if it were all true, it would not justify suspension without even a hearing. That McAdams is a right-wing creep is not grounds for his being sanctioned for his speech. Particularly odd is Weinberg's complaint that McAdams failed to show "any concern for Abbate’s welfare or future academic career." But McAdams has no obligation whatsoever to be concerned about this: Abbate is not his student, indeed, is not even in his department. The idea that this is a sanctionable offense on McAdams's part is, itself, a symptom of the New Infantilism, for which Weinberg's blog has become a leading cyber-cheerleader (though to his credit, he permits fairly wide-ranging discussion in the comments).