When, if ever, do law professors have an expectation of privacy in what they say to a student?
The answer to this question turns on four factors. First, how many people are present? Second, could the communication be overheard by a nosy listener unaided by technology, i.e., are the words spoken in "plain view." Third, is the professor acting as an employee of the law school when the communication occurs. Fourth, are the student and teacher communicating in their statuses as such.
A law professor should not think that anything he says to a large class is private. Law students trade war stories about what law professors say, they talk and send e-mails to family and friends, and they complain to the law school administration. In a large class, there could be 200 ears and 100 mouths. It's irrational to think that no one in the bunch would not publicize, as widely as possible, what the professor says. Thus, the professors comments are public, though it might upset him that the definition of public expands because of a blog.
A law professor might have an expectation of privacy in things she says in a seminar class. There the environment is more casual, with professors addressing students by their first names. Students aren't generally required to raise their hands before asking a question, as a seminar more resembles a discussion between student and teacher than a lecture. Though rigorous (my seminars were more difficult than any of the larger, lecture-style courses), seminars also have an element of monkey play not present in large lectures.
So here it is a closer call. The teacher is still on the student's tuition dime, there are several people present, and it's in "open air," that is, someone could walk by and overhear what's being said without taking measures to violate the person's privacy (as in bugging a phone). Since everything said is in "plain view," a professor who sees his words on a blog should not feel violated.
Unlike lectures or seminars, office-hours conversations should be kept private. On the one hand, the professor is using the law school's facilities, and the professor is meeting with the student in their statuses as such. (Many law students communicate with law professors, but they do not necessarily corresponding as formal student and teacher, but as friends or whatever). The vocal student might argue that he and the professor are meeting in a law school office (paid for by the student's tuition).
On the other hand, an office is more intimate than a lecture hall. Because of the closed walls, and lack of hundreds of ears, professors will generally have more open discussions. It's reasonable to think that things said in an office environment are presumptively private. This is a close call, but the professor has an expectation of privacy in things said to a student during office hours.