Cognitive impairment has been widely accepted as a disease progression measure prior to the onset of Huntington's disease. We propose a sophisticated measurement error correction method that can handle potentially correlated measurement errors in longitudinally collected exposures and multiple outcomes. The asymptotic theory for the proposed method is developed. A simulation study is conducted to demonstrate the satisfactory performance of the proposed two-stage fitting method and shows that the independent working correlation structure outperforms other alternatives. We conduct a comprehensive longitudinal analysis to assess how brain striatal atrophy affects impairment in various cognitive domains for Huntington's disease.