Cosmological N-body simulations have been a major tool of theorists for decades, yet many of the numerical issues that these simulations face are still unexplored. This paper measures numerical biases in these large, dark matter-only simulations that affect the properties of their dark matter haloes. We compare many simulation suites in order to provide several tools for simulators and analysts which help mitigate these biases. We summarise our comparisons with practical `convergence limits that can be applied to a wide range of halo properties, including halo properties which are traditionally overlooked by the testing literature. We also find that the halo properties predicted by different simulations can diverge from one another at unexpectedly high resolutions. We demonstrate that many halo properties depend strongly on force softening scale and that this dependence leads to much of the measured divergence between simulations. We offer an empirical model to estimate the impact of such effects on the rotation curves of a halo population. This model can serve as a template for future empirical models of the biases in other halo properties.
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