Web mashups are a new generation of applications based on the composition of ready-to-use, heterogeneous components. They are gaining momentum thanks to their lightweight composition approach, which represents a new opportunity for companies to leverage on past investments in SOA, Web services, and public APIs. Although several studies are emerging in order to address mashup development, no systematic mapping studies have been reported on how quality issues are being addressed. This paper reports a systematic mapping study on which and how the quality of Web mashups has been addressed and how the product quality-aware approaches have been defined and validated. The aim of this study is to provide a background in which to appropriately develop future research activities. A total of 38 research papers have been included from an initial set of 187 papers. Our results provided some findings regarding how the most relevant product quality characteristics have been addressed in different artifacts and stages of the development process. They have also been useful to detect some research gaps, such as the need of more controlled experiments and more quality-aware mashup development proposals for other characteristics which being important for the Web domain have been neglected such as Usability and Reliability.