Embedded systems are increasingly networked and distributed, often, such as in the Internet of Things (IoT), over open networks with potentially unbounded delays. A key challenge is the need for real-time guarantees over such inherently unreliable and unpredictable networks. Generally, timeouts are used to provide timing guarantees while trading off data losses and quality. The schedule of distributed task executions and network timeouts thereby determines a fundamental latency-quality trade-off that is, however, not taken into account by existing scheduling algorithms. In this paper, we propose an approach for scheduling of distributed, real-time streaming applications under quality-latency goals. We formulate this as a problem of analytically deriving a static worst-case schedule of a given distributed dataflow graph that minimizes quality loss while meeting guaranteed latency constraints. Towards this end, we first develop a quality model that estimates SNR of distributed streaming applications under given network characteristics and an overall linearity assumption. Using this quality model, we then formulate and solve the scheduling of distributed dataflow graphs as a numerical optimization problem. Simulation results with random graphs show that quality/latency-aware scheduling improves SNR over a baseline schedule by 50% on average. When applied to a distributed neural network application for handwritten digit recognition, our scheduling methodology can improve classification accuracy by 10% over a naive distribution under tight latency constraints.