A reliable automatic visual quality assessment of 3D-printed surfaces is one of the key issues related to computer and machine vision in the Industry 4.0 era. The colour-independent method based on image entropy proposed in the paper makes it possible to detect and identify some typical problems visible on the surfaces of objects obtained by additive manufacturing. Depending on the quality factor, some of such 3D printing failures may be corrected during the printing process or the operation can be aborted to save time and filament. Since the surface quality of 3D-printed objects may be related to some mechanical or physical properties of obtained objects, its fast and reliable evaluation may also be helpful during the quality monitoring procedures. The method presented in the paper utilizes the assumption of the increase of image entropy for irregularly distorted 3D-printed surfaces. Nevertheless, because of the local nature of distortions, the direct application of the global entropy does not lead to satisfactory results of automatic surface quality assessment. Therefore, the extended method, based on the combination of the local image entropy and its variance with additional colour adjustment, is proposed in the paper, leading to the proper classification of 78 samples used during the experimental verification of the proposed approach.