The power captured by a wave energy converter (WEC) can be greatly increased through the use of a well-conceived wave-by-wave control strategy. Optimal strategies including Model Predictive Control (MPC) rely on a dynamic model of the WEC and prediction of the wave excitation force several seconds into the future. Both the modelling and prediction processes are subject to errors. This study investigates the impact of these errors on the performance of a WEC under MPC. Idealised simulations are conducted to establish a suitable prediction horizon and establish a performance benchmark against an optimally tuned passively damped system. Power increases of over 200% are seen. The assumptions of perfect prediction and system modelling are progressively removed, culminating in multi-body simulation of a specific multi-DOF submerged point absorber WEC with constrained MPC. Under realistic conditions, the power gain is a more modest 30% at best across the tested sea states, demonstrating that these errors have a significant impact on performance. However, the ability to use constraints to limit motion in high energy seas and the tunability of the control law are valuable attributes for practical deployment. Overall the performance gains demonstrate the benefits of such control strategies for application to multi-DOF WECs.