Wave field synthesis is a spatial audio reproduction concept that is based on the synthesis of a wave field over an extended listening area. The reproduction of moving sound sources is an important feature for many areas of application, for instance theatres, cinemas or virtual reality applications. Although several current WFS systems are able to reproduce moving sound sources, the synthesis causes a number of distinct, audible artifacts. In this article we classify and describe these artifacts, explain their causes and discuss means to reduce audible deviations. The key question is whether the correct reproduction is possible using the theory underlying the current WFS technology. Our investigations suggest that at least one artifact, which is perceived as a spectral broadening of a moving source, cannot be solved sufficiently by the current WFS theory. This states a clear need for further research dealing specifically with the reproduction of moving sources.