Future large-scale structure surveys of the Universe will aim to constrain the cosmological model and the true nature of dark energy with unprecedented accuracy. In order for these surveys to achieve their designed goals, they will require predictions for the non-linear matter power spectrum to sub-percent accuracy. Through the use of a large ensemble of cosmological N-body simulations, we demonstrate that if we do not understand the uncertainties associated with simulating structure formation, i.e. knowledge of the 'optimal' simulation parameters, and simply seek to marginalize over them, then the constraining power of such future surveys can be significantly reduced. However, for the parameters {n s , h, Ω b , Ω m }, this effect can be largely mitigated by adding the information from a cosmic microwave background experiment, like Planck. In contrast, for the amplitude of fluctuations σ8 and the time-evolving equation of state of dark energy {w 0, w a }, the mitigation is mild. On marginalizing over the simulation parameters, we find that the dark-energy figure of merit can be degraded by ∼2. This is likely an optimistic assessment, since we do not take into account other important simulation parameters. A caveat is our assumption that the Hessian of the likelihood function does not vary significantly when moving from our adopted to the optimal simulation parameter set. This paper therefore provides strong motivation for rigorous convergence testing of N-body codes to meet the future challenges of precision cosmology.