Problem definition: Inaccurate records of inventory occur frequently and, by some measures, cost retailers approximately 4% in annual sales. Detecting inventory inaccuracies manually is cost-prohibitive, and existing algorithmic solutions rely almost exclusively on learning from longitudinal data, which is insufficient in the dynamic environment induced by modern retail operations. Instead, we propose a solution based on cross-sectional data over stores and stock-keeping units (SKUs), viewing inventory inaccuracies as a problem of identifying anomalies in a (low-rank) Poisson matrix. State-of-the-art approaches to anomaly detection in low-rank matrices apparently fall short. Specifically, from a theoretical perspective, recovery guarantees for these approaches require that nonanomalous entries be observed with vanishingly small noise (which is not the case in our problem and, indeed, in many applications). Methodology/results: So motivated, we propose a conceptually simple entrywise approach to anomaly detection in low-rank Poisson matrices. Our approach accommodates a general class of probabilistic anomaly models. We show that the cost incurred by our algorithm approaches that of an optimal algorithm at a min-max optimal rate. Using synthetic data and real data from a consumer goods retailer, we show that our approach provides up to a 10× cost reduction over incumbent approaches to anomaly detection. Along the way, we build on recent work that seeks entrywise error guarantees for matrix completion, establishing such guarantees for subexponential matrices, a result of independent interest. Managerial implications: By utilizing cross-sectional data at scale, our novel approach provides a practical solution to the issue of inventory inaccuracies in retail operations. Our method is cost-effective and can help managers detect inventory inaccuracies quickly, leading to increased sales and improved customer satisfaction. In addition, the entrywise error guarantees that we establish are of interest to academics working on matrix-completion problems. History: This paper was selected for Fast Track in M&SOM from the 2022 MSOM Supply Chain Management SIG Conference. Funding: Financial support from the National Science Foundation Division of Civil, Mechanical, and Manufacturing Innovation [Grant CMMI 1727239] is gratefully acknowledged. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0146 .