The general level of argument people use is fairly low. Looking that the Chronicle of Higher Education comment threads, I notice people will make arguments like this. (Irrespective of whether I happen to agree with the perspective: obviously it is easier to spot fallacies when you are looking to discount a particular point of view, but I find people I agree with can be equally fallacious.)
Arguments from anecdote or limited information, with no empirical foundation. This happened to me, so this must be typical. "My grandfather smoked everyday and lived to be 90."
Arguments from self-interest. Tenure is a good thing... because I have tenure!
Arguments from what "studies show," or from what a particular study showed that I read about recently, heard about on NPR or in the CHE, or from a press release from my Uni.
Overgeneralization from studies with very limited, barely significant findings. A 5% variance becomes an absolute. If men are 5% more likely to do x than women, that means "men do it and women don't."
Arguments from received wisdom or prejudice. Of course tenured professors are not going to be good teachers, because they do research. Everyone knows this already.
Arguments from the fallibility of science. Of course, you can't believe these scientific studies, because... Hitler used scientists to his ends.
Arguments from the infallibility of science. I am right because ... science! (Even when it is merely a limited form of social science of limited validity.)
Various other kinds of lazy thinking. Tenure protects academic freedom (yes, sure but is that what it mainly does in today's climate? does it really protect freedom all that well, who benefits from that type of argument?; does that mean the untenured should have no freedom?) The military protects "freedom," (but is a militarized society generally more "free"? I don't think so.)