In this paper, we evaluate the factors that influence the accuracy of lead (Pb)-isotopic ages of meteorites, and may possibly be responsible for inconsistencies between Pb-isotopic and extinct nuclide timescales of the early Solar System: instrumental mass fractionation and other possible analytical sources of error, presence of more than one component of non-radiogenic Pb, migration of ancient radiogenic Pb by diffusion and other mechanisms, possible heterogeneity of the isotopic composition of uranium (U), uncertainties in the decay constants of uranium isotopes, possible presence of "freshly synthesized" actinides with short half-life (e.g. ²³⁴U) in the early Solar System, possible initial disequilibrium in the uranium decay chains, and potential fractionation of radiogenic Pb isotopes and U isotopes caused by alpha-recoil and subsequent laboratory treatment. We review the use of ²³²Th/²³⁸U values to assist in making accurate interpretations of the U-Pb ages of meteorite components. We discuss recently published U-Pb dates of calcium-aluminum-rich inclusions (CAIs), and their apparent disagreement with the extinct nuclide dates, in the context of capability and common pitfalls in modern meteorite chronology. Finally, we discuss the requirements of meteorites that are intended to be used as the reference points in building a consistent time scale of the early Solar System, based on the combined use of the U-Pb system and extinct nuclide chronometers.