<p>Massive datasets are not only frequently affected by measurement errors, but also subject to model misspecification. This paper investigates optimal Poisson subsampling strategy for misspecified measurement error models with massive data. For a pre-specified target parameter, we advocate specifying two linear regression models for both the response and the covariate of interest and then a subsampling double-robust score function is formulated. We show that the resulting subsample estimator is consistent and asymptotically normal when either one of the postulated models is correct. The optimal Poisson subsampling probabilities are derived based on a unified criterion that encompasses both A- and L-optimality criteria, and a practical two-step algorithm is proposed to facilitate their application. Furthermore, in scenarios involving massive datasets distributed across multiple sites, we refine our proposed subsampling score function to be heterogeneity-aware for the common parameter within each site while controlling for other site-specific nuisance functions. The effectiveness of the proposed Poisson subsample estimators is demonstrated through both simulation studies and a real-world application.</p>