In recent years, GRENOUILLE has emerged as a relatively simple technique to fully characterize the electric field of an ultrashort laser pulse in a single shot. It does so by spatially mapping the delays on the transverse spatial coordinate and by mapping the frequencies on the angular coordinate of the orthogonal direction. Because of this spatial mapping, an aberrated wavefront could distort and affect the measurement of the pulse. It is shown here experimentally how these aberrations can affect the measurement using a deformable mirror to induce various aberrations in the wavefront. This can result in distortions of the spectral or temporal profile of the retrieved pulse, and a decrease of the intensity of the second-harmonic signal generated by the nonlinear crystal. Additionally, the signatures of some of the distortions of the trace resemble those previously identified as being caused by pulse-front tilt or spatial chirp and could be interpreted as such while being in fact caused by aberrations. This can complicate the identification of the real source of the distortions, since a purely spatial effect can cause distortions similar to those created by dispersion-based phenomena or other types of spatiotemporal couplings.