We diagnose relational grounding failures in zero-shot English-to-Chinese dialogue summarization with small language models (SLMs). We develop and apply a Dialogue-Semantic Grounding Error Taxonomy to evaluate three open-weight SLMs alongside a supervised mBART baseline. The taxonomy captures errors in entities, events, speaker roles, circumstances, modality, discourse outcomes, omissions, and language or format issues. Our analysis shows that SLM hallucinations often involve relation-sensitive distortions of dialogue-relevant content: models may preserve source-relevant participants, events, or circumstances while altering who did what, under what conditions, or with what outcome. These findings position the taxonomy as a diagnostic evaluation framework for dialogue summarization, revealing relation-sensitive faithfulness failures that reference-based metrics may obscure.