This paper investigates how network and traffic heterogeneities influence the accuracy of a simulation based on the Macroscopic Fundamental Diagram (MFD). To this end, the MFD modeling of a simple grid network is compared to the outputs of a mesoscopic kinematic wave model simulating traffic in the same network. Heterogeneous distributions of demand and supply at the boundaries are set to the local entries and exits of the mesoscopic model to generate heterogeneous network loadings. These boundary conditions challenge the MFD simulation, as significant discrepancies are observed between both modeling approaches in steady state. While the accurate calibration of the MFD and the average trip length can reduce the discrepancies for heterogeneous demand settings, no simple solution exists for heterogeneous supply settings, because they may drive very different internal congestion patterns in the network. We propose a correction method to adjust the MFD model outputs in such a case.