Errors in labels obtained via human annotation adversely affect a trained model's performance. Existing approaches propose ways to mitigate the effect of label error on a model's downstream accuracy, yet little is known about its impact on a model's group-based disparity metrics\footnote{Group-based disparity metrics like subgroup calibration, false positive rate, false negative rate, equalized odds, and equal opportunity are more often known, colloquially, as \textit{fairness metrics} in the literature. We use the term group-based disparity metrics in this work.}. Here we study the effect of label error on a model's group-based disparity metrics like group calibration. We empirically characterize how varying levels of label error, in both training and test data, affect these disparity metrics. We find that group calibration and other metrics are sensitive to train-time and test-time label error---particularly for minority groups. For the same level of label error, the percentage change in group calibration error for the minority group is on average 1.5 times larger than the change for the majority group. Towards mitigating the impact of training-time label error, we present an approach to estimate how changing a single training input's label affects a model's group disparity metric on a test set. We empirically assess the proposed approach on a variety of datasets and find a 10-40\% improvement, compared to alternative approaches, in identifying training inputs that improve a model's disparity metric. The proposed approach can help surface training inputs that may need to be corrected for improving a model's group-based disparity metrics.