Context: Nowadays, the prediction of source code design problems plays an essential role in the software development industry, identifying defective architectural modules in advance. For this reason, some studies explored this subject in the last decade. Researchers and practitioners often need to create an overview of such studies considering the predictors of design problems, their main contributions, the used prediction techniques and research methods. Problem: However, the current literature remains scarce of studies proposing a detailed mapping of studies already published. Objective: This article, therefore, focuses on classifying the current literature and pinpointing trends and challenges worth investigating in this research field. Method: A systematic mapping of the literature was designed and performed based on well-established practical guidelines. In total, 35 primary studies were selected, analyzed, and categorized after applying a careful filtering process from a corpus of 894 candidate studies to answer six research questions. Results: The main results are that a majority of the primary studies (1) explore Bloater bad smells, (2) use code complexity and size as predictors, (3) apply machine learning techniques to generate predictions, and (4) present a prediction proposal without an extensive empirical assessment. Conclusions: Predicting design problems is still in its infancy, showing that there is plenty of room for future work. Finally, this study can serve as a starting point for the research community