A video-grounded dialogue system is required to understand both dialogue, which contains semantic dependencies from turn to turn, and video, which contains visual cues of spatial and temporal scene variations. Building such dialogue systems is a challenging problem, involving various reasoning types on both visual and language inputs. Existing benchmarks do not have enough annotations to thoroughly analyze dialogue systems and understand their capabilities and limitations in isolation. These benchmarks are also not explicitly designed to minimise biases that models can exploit without actual reasoning. To address these limitations, in this paper, we present DVD, a Diagnostic Dataset for Video-grounded Dialogues. The dataset is designed to contain minimal biases and has detailed annotations for the different types of reasoning over the spatio-temporal space of video. Dialogues are synthesized over multiple question turns, each of which is injected with a set of cross-turn semantic relationships. We use DVD to analyze existing approaches, providing interesting insights into their abilities and limitations. In total, DVD is built from $11k$ CATER synthetic videos and contains $10$ instances of $10$-round dialogues for each video, resulting in more than $100k$ dialogues and $1M$ question-answer pairs. Our code and dataset are publicly available at https://github.com/facebookresearch/DVDialogues.