Point process models such as the epidemic-type aftershock sequence (ETAS) model have been widely used to analyze and describe seismic catalogs and to perform short-term forecasting. The standard errors of parameter estimates in the ETAS model are significant and cannot be ignored. This paper uses simulations to explore the accuracy of conventional standard error estimates based on the Hessian matrix of the log-likelihood function of the ETAS model. We show that such error estimates are not accurate when the observed space-time window is small. One must only cautiously trust the Hessian-based standard error estimates for this model when using local datasets with time windows of several years in length. The standard errors for all parameter estimates introduced by magnitude errors in typical earthquake catalogs are found to be smaller than those introduced by choosing a finite time window. However, neither effect is insignificant.