When assessment tasks are set for students in universities and colleges, a common practice is to advise them of the criteria that will be used for grading their responses. Various schemes for using multiple criteria have been widely advocated in the literature. Each scheme is designed to offer clear benefits for students. Breaking down holistic judgments into more manageable parts is seen as a way to increase openness for students and achieve more objectivity in grading. However, such approaches do not adequately represent the full complexity of multi-criterion qualitative judgments, and can lead to distorted grading decisions. Six anomalies in the ways assessors approach the grading task are identified, together with several likely contributing factors. Overall, the conclusion is that explicit grading models do not have as strong a theoretical foundation as is commonly supposed, and that holistic appraisal merits further investigation.