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Recent work has identified noisy and misannotated data as a core cause of hallucinations and unfaithful outputs in Natural Language Generation (NLG) tasks. Consequently, identifying and removing these examples is a key open challenge in creating reliable NLG systems. In this work, we introduce a framework to identify and remove low-quality training instances that lead to undesirable outputs, such as faithfulness errors in text summarization. We show that existing approaches for error tracing, such as gradient-based influence measures, do not perform reliably for detecting faithfulness errors in NLG datasets. We overcome the drawbacks of existing error tracing methods through a new, contrast-based estimate that compares undesired generations to human-corrected outputs. Our proposed method can achieve a mean average precision of 0.93 at detecting known data errors across synthetic tasks with known ground truth, substantially outperforming existing approaches. Using this approach and re-training models on cleaned data leads to a 70% reduction in entity hallucinations on the NYT dataset and a 55% reduction in semantic errors on the E2E dataset.