New devices in smart grid such as smart meters and sensors have emerged to become a massive and complex network, where a large volume of data is flowing to the smart grid systems. Those data can be real-time, fast-moving, and originated from a vast variety of terminal devices. However, the big smart grid data also bring various data quality problems, which may cause the delayed, inaccurate analysis of results, even fatal errors in the smart grid system. This paper, therefore, identifies a comprehensive taxonomy of typical data quality problems in the smart grid. Based on the adaptation of established data quality research and frameworks, this paper proposes a new data quality management framework that classifies the typical data quality problems into related data quality dimensions, contexts, as well as countermeasures. Based on this framework, this paper not only provides a systematic overview of data quality in the smart grid domain, but also offers practical guidance to improve data quality in smart grids such as which data quality dimensions are critical and which data quality problems can be addressed in which context.