Large clinical studies, particularly those utilizing electronic health records, can be subject to correlated measurement error in a covariate and failure time outcome. Errors of this nature can be corrected by carefully reviewing medical records; however, this is expensive and time-consuming to do for a large number of records. Instead, we can perform data validation on a subset of records to obtain correct estimates. While methods to analyze such two-phase designs have been well-studied, less attention has been given to efficient sampling designs to select the phase two subjects, in particular for the complex setting of errors in a continuous time-to-event, observed event indicator, and covariate that are correlated. We consider the case-cohort, stratified, balanced, and counter-matching sampling designs and develop extensions of those to our failure time measurement error setting. Detailed numerical studies are presented to examine the efficiency of the designs compared to simple random sampling under varying scenarios of the level of censoring, error structure, validation subset size, and strength of association. We further illustrate our method with an application to real data.