Digital Elevation Models (DEM) are widely used in planetary sciences, including for the specific case of Mars. DEMs allow us to extract topography parameters necessary in geomorphological studies. However, DEMs are not free from vertical errors, which yields uncertainties in calculations of parameters such as local slopes. In addition, slope maps computed from DEMs often display slope patterns which are not spatially correlated with the original images. We suspect such slope patterns to originate from DEM vertical errors. To investigate this question, we propose a fully numerical method to provide a quantitative analysis of slope errors based on DEM error propagation using synthetic models. We find that the addition of vertical errors following a normal distribution (random noise) leads to the occurrence of slope patterns comparable to those in observed data. Results are similar for the two models of spatially correlated errors. We also provide estimations of slope errors for four martian cameras: HiRISE (High Resolution Imaging Science Experiment), CaSSIS (Colour and Stereo Surface Imaging System), HRSC (High Resolution Stereo Camera) and MOC (Martian Orbiter Camera). These estimations aim to be used as first order uncertainty constraints on local slopes for geomorphological studies.