The integrity of the machined surface in precision wire electrical discharge machining (WEDM) of electrically conductive materials is one of the most important quality indicators. The integrity parameters of the machined surface are primarily monitored in terms of micro and macro geometry parameters. This paper presents the results obtained as a part of experimental research aimed at evaluating surface crack density (SCD) when machining EN HS6-5-2C using WEDM technology. The aim was to find a combination of main technological parameters (MTP) in order to minimize the qualitative indicators SCD and Ra of the eroded surface. The results of experimental research within the framework of the evaluation of SCD and Ra indicators were processed using the Taguchi method. The integrity of the eroded surface was examined by scanning digital microscope (SDM) after application of full and multiple offset cuts with an AC Brass LP 1000 brass wire electrode. Based on the experimental measurements performed, significant facts were discovered. It was found that the largest surface integrity defects are present after the application of full cuts and the first two offset cuts. At the same time, it was found that lower values of the SCD parameter in WEDM of EN HS6-5-2C steel were recorded at thicknesses above 130.0 mm. The SCD parameter was also confronted with the Ra parameter, and it was found that they are significantly influenced by MTP. The higher value of the peak current I (19 A) and the longer duration of the discharge ton (32 μs) result in an increase in the value of the SCD parameter from 0.005 μm·μm−2 to 0.0256 μm·μm−2. The resulting solutions are mathematical regression models (MRM), which allow the prediction of both monitored qualitative indicators with respect to their minimization.