The differential adhesion hypothesis (DAH) explains cell sorting and related cell rearrangements as progressions of motile and mutually adhesive cell populations toward configurations of minimal interfacial (adhesive) free energy. Many behavioral predictions based upon this hypothesis have been confirmed. However, elements of the hypothesis itself have been misunderstood by some authors, who have consequently erred in their expectations of the behavior it would predict. One commonly held misconception is that this hypothesis entails an assumption that all cells adhere to one another through a common chemical mechanism. Other errors have been introduced in connection with the interpretation of the results of computer simulations of cell sorting. In general, when a computer simulation based upon the DAH has failed to generate all of the expected behavior, there has been a tendency to attribute this to shortcomings of the DAH itself. It is here shown, however, that the difficulty, in each instance of which I am aware, has lain either in faulty understanding of the behavior actually displayed by living cell populations as they sort out, or in some inadequacy of the simplified rules fed to the computer. When these deficiences are corrected, DAH-based computer simulations of cell sorting, although awkward, nevertheless produce fairly lifelike approximations of cell-sorting behavior.