Distant Supervision (DS) is a promising learning approach for MRC by leveraging easily-obtained question-answer pairs. Unfortunately, the heuristically annotated dataset will inevitably lead to mislabeled instances, resulting in answer bias and context noise problems. To learn debiased and denoised MRC models, this paper proposes the Contrastive Distant Supervision algorithm – CDS, which can learn to distinguish confusing and noisy instances via confidence-aware contrastive learning. Specifically, to eliminate answer bias, CDS samples counterfactual negative instances, which ensures that MRC models must take both answer information and question-context interaction into consideration. To denoise distantly annotated contexts, CDS samples confusing negative instances to increase the margin between correct and mislabeled instances. We further propose a confidence-aware contrastive loss to model and leverage the uncertainty of all DS instances during learning. Experimental results show that CDS is effective and can even outperform supervised MRC models without manual annotations.