In this paper, we present a global-to-local task-aware fault detection and identification algorithm to detect failures in a multi-spacecraft system performing a collaborative inspection (referred to as global) task. The inspection task is encoded as a cost functional $\costH$ that informs global (task allocation and assignment) and local (agent-level) decision-making. The metric $\costH$ is a function of the inspection sensor model, and the agent full-pose. We use the cost functional $\costH$ to design a metric that compares the expected and actual performance to detect the faulty agent using a threshold. We use higher-order cost gradients $\costH$ to derive a new metric to identify the type of fault, including task-specific sensor fault, an agent-level actuator, and sensor faults. Furthermore, we propose an approach to design adaptive thresholds for each fault mentioned above to incorporate the time dependence of the inspection task. We demonstrate the efficacy of the proposed method empirically, by simulating and detecting faults (such as inspection sensor faults, actuators, and sensor faults) in a low-Earth orbit collaborative spacecraft inspection task using the metrics and the threshold designed using the global task cost $\costH$.