A rapid development and growing popularity of additive manufacturing technology leads to new challenging tasks allowing not only a reliable monitoring of the progress of the 3D printing process but also the quality of the printed objects. The automatic objective assessment of the surface quality of the 3D printed objects proposed in the paper, which is based on the analysis of depth maps, allows for determining the quality of surfaces during printing for the devices equipped with the built-in 3D scanners. In the case of detected low quality, some corrections can be made or the printing process may be aborted to save the filament, time and energy. The application of the entropy analysis of the 3D scans allows evaluating the surface regularity independently on the color of the filament in contrast to many other possible methods based on the analysis of visible light images. The results obtained using the proposed approach are encouraging and further combination of the proposed approach with camera-based methods might be possible as well.