In this study, we reexamined the wetting behavior of Ne adsorbed on a solid Mg surface. In a recent study, Zhou and Zhang (J. Phys. Chem. Solids, 2017, 103, 123) reported an investigation of this system. They proposed an adsorption potential, φ_ext(z), and studied this system based on augmented density functional theory (DFT) to determine the wetting temperature T_w and critical prewetting temperature T_cpw. The value obtained for T_cpw differed greatly from that produced by Grand Canonical Monte Carlo simulations (Phys. Rev. E, 1999, 59, 864) and previous DFT calculations (Phys. Rev. E, 2009, 79, 011603). In the present study, we calculated the adsorption isotherms with the Kierlik.Rosinberg DFT for two different external potentials, i.e., the aforementioned φ_ext(z) and the proposed ab initio Chizmeshya-Cole-Zaremba (CCZ) potential. This study had two main aims. First, we aimed to identify the main sources of the discrepancies between the results obtained by Zhou and Zhang and those produced in other studies. Second, we analyzed the new data computed with the CCZ potential by applying the so-called arc-length continuation method. The new results supported the old ones, yielding more accurate values for both characteristic temperatures and indicating interesting new features of the system. We developed a novel alternative procedure for determining an appropriate value of T_cpw for moderately strong adsorbers. Assuming that Ne is liquid in the range of T_w ≲ T < T_t, then the DFT calculations were extended into this region. We showed that close to T_t and after the prewetting jump, the growth of the films exhibited a sequence of layering transitions, which originated coalescent prewetting lines.