A comprehensive analysis of the resolution effects of a cross-wire probe for velocity measurements is presented. The results, which are obtained from DNS of isotropic turbulence and from a model spectrum of the turbulent kinetic energy, consider different lengths of the wires, separations between the wires, as well as time sampling rates of the velocity signal. The impact of the resolution is estimated on several quantities, such as the velocity variance, the velocity derivative variance and some isotropy estimators. In general, the lack of resolution has a larger effect on the statistics of the velocity derivatives. However, it is found that a particular surrogate of the kinetic energy dissipation rate remains relatively unaffected even when the separation between the wires is large. Further, the correction factors derived from the model spectrum systematically overcorrect the underresolved measurements.