Context-aware applications that are responsive to the physical world can be effectively supported by Complex Event Processing (CEP). Distributed CEP (DCEP) efficiently detects situations based on real-world events from widely distributed event sources. Unfortunately, due to uncertain event data from the physical world, unreliable event sources and unreliable event communication, DCEP often cannot provide correct and complete situation detection. Until now, DCEP systems have not paid sufficient attention to this problem. In this paper, we present a quality-aware distributed CEP system which provides context-aware applications with a reasonable quality measure for the complex events it detects. It employs a description for the uncertainty and imprecision of event data and quality measures for event sources and event communication, to detect complex events and determine their quality. Based on the quality descriptions for events and event data, context-aware applications can reasonably decide to what degree to rely on detected complex events.