Dialogue summarization comes with its own peculiar challenges as opposed to news or scientific articles summarization. In this work, we explore four different challenges of the task: handling and differentiating parts of the dialogue belonging to multiple speakers, negation understanding, reasoning about the situation, and informal language understanding. Using a pretrained sequence-to-sequence language model, we explore speaker name substitution, negation scope highlighting, multi-task learning with relevant tasks, and pretraining on in-domain data. Our experiments show that our proposed techniques indeed improve summarization performance, outperforming strong baselines.