This brief note calls attention to the literature discussing four pedagogical points relating to the application and teaching of the well-known Gibbs phase rule: (i) suggestions that the component term be broken into a species term, an equilibrated reaction term, and an independent stoichiometric constraint term; (ii) suggestions that the number of intensive fields be left as a variable rather than being automatically set at a value of two; (iii) debates on whether the rule needs further modification when dealing with optical enantiomers; and (iv) questions of whether textbook problems that ask students to predict the degrees of freedom ahead of time are realistic.