Checklists are interpretable and easy-to-deploy models often used in real-world clinical decision-making. Prior work has demonstrated that checklists can be learned from binary input features in a data-driven manner by formulating the training objective as an integer programming problem. In this work, we learn diagnostic checklists for the task of phenotype classification with time series vitals data of ICU patients from the MIMIC-IV dataset. For 13 clinical phenotypes, we fully explore the empirical behavior of the checklist model in regard to multimodality, time series dynamics, and fairness. Our results show that the addition of the imaging data modality and the addition of shapelets that capture time series dynamics can significantly improve predictive performance. Checklist models optimized with explicit fairness constraints achieve the target fairness performance, at the expense of lower predictive performance.