Social media has become an essential part of the daily routines of children and adolescents. Moreover, enormous efforts have been made to ensure the psychological and emotional well-being of young users as well as their safety when interacting with various social media platforms. In this paper, we investigate the exposure of those users to inappropriate comments posted on YouTube videos targeting this demographic. We collected a large-scale dataset of approximately four million records and studied the presence of five age-inappropriate categories and the amount of exposure to each category. Using natural language processing and machine learning techniques, we constructed ensemble classifiers that achieved high accuracy in detecting inappropriate comments. Our results show a large percentage of worrisome comments with inappropriate content: we found 11% of the comments on children's videos to be toxic, highlighting the importance of monitoring comments, particularly on children's platforms.