Generative single-image super-resolution (SISR) is advancing rapidly, yet even state-of-the-art models produce visual artifacts: unnatural patterns and texture distortions that degrade perceived quality. These defects vary widely in perceptual impact--some are barely noticeable, while others are highly disturbing--yet existing detection methods treat them equally. We propose characterizing artifacts by their prominence to human observers rather than as uniform binary defects. We present a novel dataset of 1302 artifact examples from 11 SISR methods annotated with crowdsourced prominence scores, and provide prominence annotations for 593 existing artifacts from the DeSRA dataset, revealing that 48% of them go unnoticed by most viewers. Building on this data, we train a lightweight regressor that produces spatial prominence heatmaps. We demonstrate that our method outperforms existing detectors and effectively guides SR model fine-tuning for artifact suppression. Our dataset and code are available at https://tinyurl.com/2u9zxtyh.