Fatal accidents are a major issue hindering the wide acceptance of safety-critical systems that employ machine learning and deep learning models, such as automated driving vehicles. In order to use machine learning in a safety-critical system, it is necessary to demonstrate the safety and security of the system through engineering processes. However, thus far, no such widely accepted engineering concepts or frameworks have been established for these systems. The key to using a machine learning model in a deductively engineered system is decomposing the data-driven training of machine learning models into requirement, design, and verification, particularly for machine learning models used in safety-critical systems. Simultaneously, open problems and relevant technical fields are not organized in a manner that enables researchers to select a theme and work on it. In this study, we identify, classify, and explore the open problems in engineering (safety-critical) machine learning systems --- that is, in terms of requirement, design, and verification of machine learning models and systems --- as well as discuss related works and research directions, using automated driving vehicles as an example. Our results show that machine learning models are characterized by a lack of requirements specification, lack of design specification, lack of interpretability, and lack of robustness. We also perform a gap analysis on a conventional system quality standard SQuARE with the characteristics of machine learning models to study quality models for machine learning systems. We find that a lack of requirements specification and lack of robustness have the greatest impact on conventional quality models.