One of the major challenges in spatial epidemiologic studies is uncertainty in exposure measurement due to geocoding errors. Faulty geocodes in built environment data introduce errors to exposure assessments and induce bias in the inference about corresponding health effect estimates. In this study, we focus on the estimation of the health effect associated with individuals’ exposure to the food environment, represented by the number of specific food outlets within a buffer area around the subject. We show, algebraically and through simulation studies, that coarsening of food outlets’ coordinates results in exposure measurement error that has heterogeneous variance and has non-zero mean. In turn, the bias in the health effect can be away from the null in many circumstances. We extend the simulation extrapolation (SIMEX) method to correct the bias in the health effect to accommodate the non-standard measurement error distribution, without requiring external data. We illustrate the procedure with our motivating example about adult BMI in an elderly cohort and proximity to healthy food outlets near their home.