|The Covid-19 pandemic has led to a health crisis with 90 million infections and two million deaths by the end of January 2021. To prevent an overload of medical capacities, quickly identifying potentially infected persons is vital to stop the spread of the virus. Mobile apps for tracing people's contacts seem effective, but raise public concerns, e. g., about privacy. Hence, they are contested in public discourse. We report a large-scale NLP-supported analysis of people's comments about the German contact-tracing app on news websites, social media and app stores. We identified prevalent topics, stances, and how commenting developed over time. We found privacy to be among the most debated topics discussed from various perspectives. Commenting peaked at one point in time, when public discourse centered on the potential tracing protocols and their privacy protection. We encourage further research on the link between the public discussions and actual adoption rates of the app.