As a continuation of our efforts towards tackling the problem of spoken Dialect Identification (DID) for Arabic languages, we present the QCRI-MIT Advanced Dialect Identification System (QMDIS). QMDIS is an automatic spoken DID system for Dialectal Arabic (DA). In this paper, we report a comprehensive study of the three main components used in the spoken DID task: phonotactic, lexical and acoustic. We use Support Vector Machines (SVMs), Logistic Regression (LR) and Convolutional Neural Networks (CNNs) as backend classifiers throughout the study. We perform all our experiments on a publicly available dataset and present new state-of-the-art results. QMDIS discriminates between the five most widely used dialects of Arabic: namely Egyptian, Gulf, Levantine, North African, and Modern Standard Arabic (MSA).We report ≈73% accuracy for system combination. All the data and the code used in our experiments are publicly available for research.