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We address key challenges in Dataset Aggregation (DAgger) for real-world contact- rich manipulation: how to collect informative human correction data and how to effectively update policies with this new data. We introduce Compliant Residual DAgger (CR-DAgger), which contains two novel components: 1) a Compliant Intervention Interface that leverages compliance control, allowing humans to pro- vide gentle, accurate delta action corrections without interrupting the ongoing robot policy execution; and 2) a Compliant Residual Policy formulation that learns from human corrections while incorporating force feedback and force control. Our system significantly enhances performance on precise contact-rich manipu- lation tasks using minimal correction data, improving base policy success rates by over 60% on two challenging tasks (book flipping and belt assembly) while outperforming both retraining-from-scratch and finetuning approaches. Through extensive real-world experiments, we provide practical guidance for implementing effective DAgger in real-world robot learning tasks.