Matrix completion has gained considerable interest in recent years. The goal of matrix completion is to predict the unknown entries of a partially observed matrix using its known entries. Although common applications feature discrete rating-scale data, such as user-product rating matrices in recommender systems or surveys in the social and behavioral sciences, methods for matrix completion are almost always designed for and studied in the context of continuous data. Furthermore, only a small subset of the literature considers matrix completion in the presence of corrupted observations despite their common occurrence in practice. Examples include attacks on recommender systems (i.e., malicious users deliberately manipulating ratings to influence the recommender system to their advantage), or careless respondents in surveys (i.e., respondents providing answers irrespective of what the survey asks of them due to a lack of attention). We introduce a matrix completion algorithm that is tailored towards the discrete nature of rating-scale data and robust to the presence of corrupted observations. In addition, we investigate the performance of the proposed method and its competitors with discrete rating-scale (rather than continuous) data as well as under various missing data mechanisms and types of corrupted observations.