In Model-Based Diagnosis, a diagnostic algorithm is typically used to compute diagnoses using a model of a real-world system and some observations. Contrary to classical hypothesis, in real-world applications it is sometimes the case that either the model, the observations or the diagnostic algorithm are abnormal with respect to some required properties; with possibly huge economical consequences. Determining which abnormalities exist constitutes a meta-diagnostic problem. We contribute, first, with a general theory of meta-diagnosis with clear semantics to handle this problem. Second, we propose a series of typically required properties and relate them between themselves. Finally, using our meta-diagnostic framework and the studied properties and relations, we model and solve some common meta-diagnostic problems.