Factual inconsistencies in generated summaries severely limit the practical applications of abstractive dialogue summarization. Although significant progress has been achieved by using pre-trained neural language models, substantial amounts of hallucinated content are found during the human evaluation. In this work, we first devised a typology of factual errors to better understand the types of hallucinations generated by current models and conducted human evaluation on popular dialog summarization dataset. We further propose a training strategy that improves the factual consistency and overall quality of summaries via a novel contrastive fine-tuning, called CONFIT. To tackle top factual errors from our annotation, we introduce additional contrastive loss with carefully designed hard negative samples and self-supervised dialogue-specific loss to capture the key information between speakers. We show that our model significantly reduces all kinds of factual errors on both SAMSum dialogue summarization and AMI meeting summarization. On both datasets, we achieve significant improvements over state-of-the-art baselines using both automatic metrics, ROUGE and BARTScore, and human evaluation.