Recent advances in quantum computing have sparked excitement that this new computing paradigm could solve previously intractable problems. However, due to the faulty nature of current quantum hardware and quantum-intrinsic noise, the full potential of quantum computing is still years away. Hybrid quantum-classical computing has emerged as a possible compromise that achieves the best of both worlds. In this paper, we look at hybrid quantum-classical computing from a software engineering perspective and present the first empirical study focused on characterizing and evaluating recurrent issues faced by developers of hybrid quantum-classical applications. The study comprised a thorough analysis of 531 real-world issues faced by developers – including software faults, hardware failures, quantum library errors, and developer mistakes – documented in discussion threads from forums dedicated to quantum computing. By qualitatively analyzing such forum threads, we derive a comprehensive taxonomy of recurring issues in hybrid quantum-classical applications that can be used by both application and platform developers to improve the reliability of hybrid applications. The study considered how these recurring issues manifest and their causes, determining that hybrid applications are crash-dominant (74% of studied issues) and that errors were predominantly introduced by application developers (70% of issues). We conclude by identifying recurring obstacles for developers of hybrid applications and actionable recommendations to overcome them.