Computational models of motor unit populations are the objective implementations of the hypothesized mechanisms by which neural and muscle properties give rise to electromyograms (EMGs) and force. However, the variability/uncertainty of the parameters used in these models - and how they affect predictions - confounds assessing these hypothesized mechanisms. We perform a large-scale computational sensitivity analysis on the state-of-the-art computational model of surface EMG and force by combining a comprehensive review of published experimental data with Monte Carlo simulations. To exhaustively explore model performance and robustness we ran numerous iterative simulations, each using a random set of values for nine commonly measured motor neuron and muscle parameters. Parameter values were sampled across their reported experimental ranges. Convergence after 439 simulations found that only 3 simulations met our two fitness criteria: approximating the well-established experimental relations for the scaling of EMG amplitude and force variability with mean force. An additional 424 simulations preferentially sampling the neighborhood of those 3 valid simulations converged to reveal 65 additional sets of parameter values for which the model predictions approximate the experimentally known relations. The model is very sensitive to several neural properties - especially peak discharge rates and recruitment ranges. Therefore, to advance our understanding of EMG and muscle force it is critical to evaluate the hypothesized neural mechanisms as implemented in today's state-of-the-art motor unit models. We discuss experimental and analytical avenues to do so, and new features that may be added in future implementations of the model to improve its experimental validity.