Context: The dire consequences of the COVID-19 pandemic has influenced development of COVID-19 software i.e., software used for analysis and mitigation of COVID-19. Bugs in COVID-19 software can be consequential, as COVID-19 software projects can impact public health policy and user data privacy. Objective: The goal of this paper is to help practitioners and researchers improve the quality of COVID-19 software through an empirical study of open source software projects related to COVID-19. Methodology: We use 129 open source COVID-19 software projects hosted on GitHub to conduct our empirical study. Next, we apply qualitative analysis on 550 bug reports from the collected projects to identify bug categories. Findings: We identify 8 bug categories, which include data bugs i.e., bugs that occur during mining and storage of COVID-19 data. The identified bug categories appear for 7 categories of software projects including (i) projects that use statistical modeling to perform predictions related to COVID-19, and (ii) medical equipment software that are used to design and implement medical equipment, such as ventilators. Conclusion: Based on our findings, we advocate for robust statistical model construction through better synergies between data science practitioners and public health experts. Existence of security bugs in user tracking software necessitates development of tools that will detect data privacy violations and security weaknesses.