Several governments employed digital contact tracing using smartphone apps to combat the COVID-19 pandemic in 2020. Research shows that privacy concerns hinder the adoption of such apps, while privacy problems which emerged by using them are empirically unknown. This study aims to uncover the dimensions of privacy problems available in digital contact tracing through a survey from 453 citizens in Sweden. Our results show that respondents found privacy problems regarding surveillance, identification, aggregation, secondary use, disclosure, and stigma highly relevant in contact tracing apps. Among demographic factors, younger respondents were generally more concerned about privacy risks than older respondents. This study extends previous literature by revealing privacy problems arising from contact tracing apps.