This paper contains a study of the average signal-to-noise ratio that appears at the output of an optical heterodyne when the nominal centers of the signal and local oscillator beams do not coincide. It is shown that the signal-to-noise ratio is far less sensitive to this type of misalignment than it is to angular effects, and that little is accomplished by increasing the local oscillator cross section to compensate for positioning errors. A correspondence between the mixing of randomly displaced, perfectly coherent beams and the mixing of partially coherent, collinear beams is also established which yields an interesting physical interpretation of the observed results.