© 2020 Institute of Physics and Engineering in Medicine. While the pursuit of better time resolution in positron emission tomography (PET) is rapidly evolving, little work has been performed on time of flight (TOF) image quality at high time resolution in the presence of modelling inconsistencies. This works focuses on the effect of using the wrong attenuation map in the system model, causing perturbations in the reconstructed radioactivity image. Previous work has usually considered the effects to be local to the area where there is attenuation mismatch, and has shown that the quantification errors in this area tend to reduce with improved time resolution. This publication shows however that errors in the PET image at a distance from the mismatch increase with time resolution. The errors depend on the reconstruction algorithm used. We quantify the errors in the hypothetical case of perfect time resolution for maximum likelihood reconstructions. In addition, we perform reconstructions on simulated and patient data. In particular, for respiratory-gated reconstructions from a wrong attenuation map, increased errors are observed with improved time resolutions in areas close to the lungs (e.g. from 13.3% in non-TOF to up to 20.9% at 200 ps in the left ventricle).