Slide quality is an important factor in pathology workflow and diagnosis. We examine the extent of quality variations in digitized hematoxylin-eosin (H&E) slides due to variations and errors in staining and/or scanning (e.g., outof- focus blur & stitching). We propose two automatic quality estimators by adapting image quality assessment (IQA) methods that are originally developed for natural images. For the first estimator, we assume a gold-standard reference digital pathology slide is available. Quality of a given slide is estimated by comparing the slide to such a reference using a full-reference perceptual IQA method such as VIF (visual information fidelity) or SSIM (structural similarity metric). Our second estimator is based on IL-NIQE (integrated local natural image quality evaluator), a no-reference IQA, which we train using a set of artifact-free H&E high-power images (20× or 40×) from breast tissue. The first estimator (referenced) predicts marked quality reduction of images with simulated blurring as compared to the artifact-free originals used as references. The histograms of scores by the second estimator (no-reference) for images with artifact (blur, stitching, folded tissue, or air bubble artifacts) and for artifact-free images are highly separable. Moreover, the scores by the second estimator are correlated with the ratings given by a pathologist. We conclude that our approach is promising and further research is outlined for developing robust automatic quality estimators.