Inferring applicant preferences is fundamental in many analyses of school-choice data. Application mistakes make this task challenging. We propose a novel approach to deal with the mistakes in a deferred-acceptance matching environment. The key insight is that the uncertainties faced by applicants, e.g., due to tie-breaking lotteries, render some mistakes costly, allowing us to reliably infer relevant preferences. Our approach extracts all information on preferences robustly to payoff-insignificant mistakes. We apply it to school-choice data from Staten Island, NYC. Counterfactual analysis suggests that we underestimate the effects of proposed desegregation reforms when applicants' mistakes are not accounted for in preference inference and estimation.