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Robust perception is an essential component to enable long-term operation of mobile robots. It depends on failure resilience through reliable sensor data and preprocessing, as well as failure awareness through introspection, for example the ability to self-assess localization performance. This paper presents CorAl: a principled, intuitive, and generalizable method to measure the quality of alignment between pairs of point clouds, which learns to detect alignment errors in a self-supervised manner. CorAl compares the differential entropy in the point clouds separately with the entropy in their union to account for entropy inherent to the scene. By making use of dual entropy measurements, we obtain a quality metric that is highly sensitive to small alignment errors and still generalizes well to unseen environments. In this work, we extend our previous work on lidar-only CorAl to radar data by proposing a two-stage filtering technique that produces high-quality point clouds from noisy radar scans. Thus we target robust perception in two ways: by introducing a method that introspectively assesses alignment quality, and applying it to an inherently robust sensor modality. We show that our filtering technique combined with CorAl can be applied to the problem of alignment classification, and that it detects small alignment errors in urban settings with up to 98% accuracy, and with up to 96% if trained only in a different environment. Our lidar and radar experiments demonstrate that CorAl outperforms previous methods both on the ETH lidar benchmark, which includes several indoor and outdoor environments, and the large-scale Oxford and MulRan radar data sets for urban traffic scenarios The results also demonstrate that CorAl generalizes very well across substantially different environments without the need of retraining.