We reanalyze the effects of atmosphere-induced image motions on the measurement of solar polarized light using a formalism developed by Lites. Our reanalysis is prompted by the advent of adaptive optics (AO) systems that reduce image motion and higher-order aberrations, by the availability of liquid crystals as modulation devices, and by the need to understand how best to design polarimeters for future telescopes such as the Advanced Technology Solar Telescope. In this first attempt to understand the major issues, we analyze the influence of residual image motion (tip-tilt) corrections of operational AO systems on the cross talk between Stokes parameters and present results for several polarization analysis schemes. Higher-order wave-front corrections are left for future research. We also restrict our discussion to the solar photosphere, which limits several important parameters of interest, using some recent magnetoconvection simulations.