During the current COVID-19 pandemic, "digital epidemiology" has been proposed to complement traditional reporting and surveillance systems. Instruments such as smartphone contact apps, fitness trackers, and apps for voluntary reporting are intended to be used to monitor or limit the spread of COVID-19. The methodological drawbacks and limitations of these instruments and devices are insufficiently addressed in the public discussion. Therefore, we review these weaknesses and limitations, using the Total Survey Error framework to address sampling and non-sampling errors of these approaches. We argue that no useful results can be obtained by any of the suggested methods of digital epidemiology for COVID-19 research. Finally, we suggest feasible alternative data sources for valid and population covering COVID-19 indicator systems.