We propose a novel anomaly detection framework for a fleet of hybrid aerial vehicles executing high-speed package pickup and delivery missions. The detection is based on machine learning models of normal flight profiles, trained on millions of flight log measurements of control inputs and sensor readings. We develop a new scalable algorithm for robust regression which can simultaneously fit predictive flight dynamics models while identifying and discarding abnormal flight missions from the training set. The resulting unsupervised estimator has a very high breakdown point and can withstand massive contamination of training data to uncover what normal flight patterns look like, without requiring any form of prior knowledge of aircraft aerodynamics or manual labeling of anomalies upfront. Across many different anomaly types, spanning simple 3-sigma statistical thresholds to turbulence and other equipment anomalies, our models achieve high detection rates across the board. Our method consistently outperforms alternative robust detection methods on synthetic benchmark problems. To the best of our knowledge, dynamics modeling of hybrid delivery drones for anomaly detection at the scale of 100 million measurements from 5000 real flight missions in variable flight conditions is unprecedented.