Graph neural networks (GNNs) are widely used to make predictions on graph-structured data. For example, GNNs are used in spatiotemporal forecasting applications to predict extreme weather events and traffic flows. In these settings, data gathered from graph nodes is frequently noisy or missing; nodes have a true latent state (e.g. a neighborhood is flooded) that is only observed when a report is made (e.g. a resident reports the flood). We propose a GNN-based model to predict both the true latent state of nodes and the noisy observed reports. Estimating the latent state is challenging as there is a lack of ground truth data. However, in many settings we often have sparse data we can use to inform the model about the latent state. We apply our model to a case study of urban incident reporting from New York City 311 complaints with sparse latent state data sourced from government inspections. We show that by jointly modeling the true latent state and reporting rates across neighborhoods and incident types we are able to generalize to unobserved neighborhoods, types, and time periods. Our analysis reveals a widely applicable approach for using GNNs and sparse data to identify latent states.