Recent work on signal detection in graph-based data focuses on classical detection when the signal and noise are both in the form of discrete entities and their relationships. In practice, the relationships of interest may not be directly observable, or may be observed through a noisy mechanism. The effects of imperfect observations add another layer of difficulty to the detection problem, beyond the effects of typical random fluctuations in the background graph. This paper analyzes the impact on detection performance of several error and corruption mechanisms for graph data. In relatively simple scenarios, the change in signal and noise power is analyzed, and this is demonstrated empirically in more complicated models. It is shown that, with enough side information, it is possible to fully recover performance equivalent to working with uncorrupted data using a Bayesian approach, and a simpler cost-optimization approach is shown to provide a substantial benefit as well.