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Point process models have been used to analyze interaction event times on a social network, in the hope to provides valuable insights for social science research. However, the diagnostics and visualization of the modeling results from such an analysis have received limited discussion in the literature. In this paper, we develop a systematic set of diagnostic tools and visualizations for point process models fitted to data from a network setting. We analyze the residual process and Pearson residual on the network by inspecting their structure and clustering structure. Equipped with these tools, we can validate whether a model adequately captures the temporal and/or network structures in the observed data. The utility of our approach is demonstrated using simulation studies and point process models applied to a study of animal social interactions.