Instilling trust in high-stakes applications of machine learning is becoming essential. Trust may be decomposed into four dimensions: basic accuracy, reliability, human interaction, and aligned purpose. The first two of these also constitute the properties of safe machine learning systems. The second dimension, reliability, is mainly concerned with being robust to epistemic uncertainty and model mismatch. It arises in the machine learning paradigms of distribution shift, data poisoning attacks, and algorithmic fairness. All of these problems can be abstractly modeled using the theory of mismatched hypothesis testing from statistical signal processing. By doing so, we can take advantage of performance characterizations in that literature to better understand the various machine learning issues.