Data narratives increasingly shape public understanding, but their failures are rarely just isolated factual errors or deceptive charts. Instead, they emerge through a broader meaning-making process in which quantitative evidence is transformed into claims, representations, and arguments. While prior work has examined these failures across disparate fields (e.g., statistics, visualization, and fact-checking), the community lacks a holistic lens to explain how these issues arise, propagate, and compound. To address this gap, we introduce TIC, a Taxonomy of Issues in Data Communication, synthesized from prior literature and refined through the qualitative annotation of 700 real-world data narratives from fact-checking sites, research datasets, and controversial media. TIC organizes recurring breakdowns across six dimensions-data, analysis, visual encoding, text, reasoning, and interpretation-and situates them within a framework spanning analysis, narrative construction, and audience reception. Alongside the taxonomy and process framework, we contribute a qualitatively annotated case corpus with coding justifications and an interactive browsing interface. Collectively, these contributions provide a structured lens for diagnosing problematic data narratives and informing future sociotechnical support for trustworthy data communication.

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