Barack Obama has at least once, uttered the sentence "I was a constitutional law professor." This has been repeated, uncritically. One of Sully's correspondents, for example. Mark Kleiman, who really ought to know better, called him a "Con. Law Prof."
As Powerline noted back in April, this is, shall we say, a bit of puffery. Obama has taught courses in constitutional law, and so in casual conversation his students might well refer to him as "Professor." But he is listed on the University of Chicago web page as "Senior Lecturer in Law." His publications page lists his two autobiographical books, but no academic work of any sort, much less any academic writings on constitutional law. Now, given his relatively strong academic credentials and the extent of affirmative action in academic hiring, if Obama had written articles about, well, pretty much anything, he would undoubtedly have been able to get hired at an elite law school in a tenure-track position. But he didn't.
Barack Obama may well know a lot more about constitutional law than the average person, or even the average lawyer. But he is not a Professor of Constitutional Law. Nor is he an assistant professor or associate professor. At most, he's an "adjunct professor," which is not the same thing at all.