There is a longstanding interest in capturing the error behaviour of object detectors by finding images where their performance is likely to be unsatisfactory. In real-world applications such as autonomous driving, it is also crucial to characterise potential failures beyond simple requirements of detection performance. For example, a missed detection of a pedestrian close to an ego vehicle will generally require closer inspection than a missed detection of a car in the distance. The problem of predicting such potential failures at test time has largely been overlooked in the literature and conventional approaches based on detection uncertainty fall short in that they are agnostic to such fine-grained characterisation of errors. In this work, we propose to reformulate the problem of finding "hard" images as a query-based hard image retrieval task, where queries are specific definitions of "hardness", and offer a simple and intuitive method that can solve this task for a large family of queries. Our method is entirely post-hoc, does not require ground-truth annotations, is independent of the choice of a detector, and relies on an efficient Monte Carlo estimation that uses a simple stochastic model in place of the ground-truth. We show experimentally that it can be applied successfully to a wide variety of queries for which it can reliably identify hard images for a given detector without any labelled data. We provide results on ranking and classification tasks using the widely used RetinaNet, Faster-RCNN, Mask-RCNN, and Cascade Mask-RCNN object detectors. The code for this project is available at https://github.com/fiveai/hardest.