The use of a coarse-grained (CG) model that is widely used in molecular dynamics simulations of biomolecular systems is investigated with respect to the dependence of a variety of quantities upon the size of the used integration time step and cutoff radius. The results suggest that when using a non-bonded interaction-cutoff radius of 1.4 nm a time step of maximally 10 fs should be used, in order not to produce energy sinks or wells. Using a too-large time step, e. g. 50 fs with a cutoff of 1.2 nm, as is done in the coarse-grained model of Marrink et al. (J. Phys. Chem. B, 2004, 108, 250 and 2007, 111, 7812), induces errors due to the linear approximation of the integrators that are commonly used to integrate the equations of motion. As a spin-o. of the investigation of the mentioned CG models, we found that the parameters of the CG water model place it at physiological temperatures well into the solid phase of the phase diagram.