The healthcare domain is one of the most exciting application areas for machine learning, but a lack of model transparency contributes to a lag in adoption within the industry. In this work, we explore the current art of explainability and interpretability within a case study in clinical text classification, using a task of mortality prediction within MIMIC-III clinical notes. We demonstrate various visualization techniques for fully interpretable methods as well as model-agnostic post hoc attributions, and we provide a generalized method for evaluating the quality of explanations using infidelity and local Lipschitz across model types from logistic regression to BERT variants. With these metrics, we introduce a framework through which practitioners and researchers can assess the frontier between a model's predictive performance and the quality of its available explanations. We make our code available to encourage continued refinement of these methods.