Automated anomaly detection in panoramic dental x-rays is a crucial step in streamlining post diagnosis treatment. It can reduce clinical time for a patient and also aid in giving them faster access to medical care. In this paper, we propose a hybrid deep learning and machine learning based approach to detect evident dental caries/periapical infection, altered periodontal bone height, and third molar impactions using panoramic dental radiographs. We use a Convolutional Neural Network as a feature extractor for an input image and use a Support Vector Machine to classify the image as either "Normal"or "Anomalous"based on the extracted features. We compare the performance of this model with the performance of a Convolutional Neural Network and a Support Vector Machine for the same classification task. We also compare our best model with other existing models trained to detect carries and periodontal bone loss. The results obtained with the hybrid deep learning and machine learning approach outperformed the existing methods in the literature.