Unlike traditional planar 2D visual content, immersive 360-degree images and videos undergo particular processing steps and are intended to be consumed via head-mounted displays (HMDs). To get a deeper understanding on the perception of 360-degree visual distortions when consumed through HMDs, we perform an exploratory task-based subjective study in which we have asked subjects to define the first noticeable difference and break-in-presence points when incrementally adding specific compression artifacts. The results of our study: give insights on the range of allowed visual distortions for 360-degree content; show that the added visual distortions are more tolerable in mono than in stereoscopic 3D; and identify issues with current 360-degree objective quality metrics.