The quality of training data is critical to the performance of machine learning models. In this paper, the Error Sensitivity Profile (ESP) is proposed. It quantifies the sensitivity of model performance to errors in a single feature or in multiple features. By leveraging ESP, data-cleaning efforts can be prioritized based on error types and features most likely to affect model performance. To support the computation of this metric, an integrated suite of tools, called \dirty, is created. We conduct an extensive experimental study on two widely used datasets using 14 classification models, revealing that performance degradation is not always predictable from simple correlations with the target variable.