We point out inconsistencies in the recent paper by Oughstun et al. on Sommerfeld and Brillouin precursors [J. Opt. Soc. Am. B 27, 1664-1670 (2010)]. Their study is essentially numerical and, for the parameters used in their simulations, the difference between the two limits considered is not as clear-cut as they state. The steep rise of the Brillouin precursor obtained in the singular limit and analyzed as a distinguishing feature of this limit simply results from an unsuitable time scale. In fact, the rise of the precursor is progressive and is perfectly described by a Airy function. In the weak dispersion limit, the equivalence relation, established at great length in Section 3 of the paper, appears as an immediate result in the retarded-time picture. Last but not least, we show that, contrary to the authors claim, the precursors are catastrophically affected by the rise-time of the incident optical field, even when the latter is considerably faster than the medium relaxation time.