Several authors have had apparent success in applying continuous‐time point process models to rainfall occurrence sequences. In this paper, it is shown that if rainfall occurrences are interpreted as the events of a point process (and not as a censored sample), the continuous‐time point process methodology and estimation procedures are not directly applicable since they fail to account for the time discreteness of the sample process. This is demonstrated analytically by studying the effects of discretization on selected statistical properties of a Poisson process, a Neyman‐Scott process, and a renewal Cox process with Markovian intensity. In general, the study of rainfall occurrences under the continuous‐time point process framework may result in misleading inferences regarding clustering (dispersion), and consequently incorrect interpretations of the underlying rainfall generating mechanisms. For example, daily rainfall occurrence structures underdispersed relative to the Poisson process are usually overdispersed relative to the Bernoulli process (the discrete‐time analogue of the Poisson). These findings are confirmed by the statistical analysis of six daily rainfall records representative of a range of U.S. climates, two of which are described in detail.