Graph neural networks (GNNs) are widely used to make predictions on graph-structured data -- e.g., in spatiotemporal forecasting applications, GNNs are used to predict extreme weather events and traffic flows. However, data from graph nodes is frequently noisy or missing; nodes have a true latent state (e.g. a neighborhood is flooded) that is observed via a report (e.g. a resident reports the flood). We propose a GNN-based model to predict both the true latent state of nodes and the observed reports. Estimating the latent state is challenging as there is a lack of ground truth data. However, 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 reporting from New York City 311 complaints with latent state data sourced from government inspections. We show that by jointly modeling the 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.