I think, you will find M. Ted, that according to the University of Chicago that Obama is entitled to call himself a "Professor of Law at the University of Chicago" Or even a "Professor of Constitutional Law at the University of Chicago", since that is precisely what he taught. but that he is not entitled to call himself a "Full Professor or a tenured Professor at the University of Chicago."

I have not read in detail exactly what he is accused of but I heard him call himself a Professor of Constitutional Law on The View and as far as I can see that is OK.