This paper develops a computationally efficient method to bound the impact of multiple uncertain parameters in a dynamic load model. Load model trajectory sensitivity is first conducted on regional dynamics only (e.g., a large industrial load bus and its model for adequately representing the bus voltage dynamics) to identify critical and correlated load parameters. Systemwide trajectory sensitivity on the entire power system model is then evaluated for this reduced set of parameters, and finally, the impact of multiple uncertain parameters on the representation of power system dynamics is bounded. To reinforce this reasoning, we elaborate on the conceptual meaning of the load model trajectory sensitivity, its implication, and its applicability to the entire power grid analysis. This research also develops a fluctuation index of trajectory sensitivity (FI-TS) to effectively rank and select the model parameters based on the impact of their perturbations on the system's dynamic performance. Case studies for the Korean power system demonstrate the validity and efficacy of the developed methods for adequately bounding the uncertainty impacts with reference to the comprehensive time-domain dynamic simulation approach.