We present a technique for phase-shifting digital in-line holography which compensates for lateral object motion. By collecting two frames of interference between object and reference fields with identical reference phase, one can estimate the lateral motion that occurred between frames using the cross-correlation. We also describe a very general linear framework for phase-shifting holographic reconstruction which minimizes additive white Gaussian noise (AWGN) for an arbitrary set of reference field amplitudes and phases. We analyze the technique's sensitivity to noise (AWGN, quantization, and shot), errors in the reference fields, errors in motion estimation, resolution, and depth of field. We also present experimental motion-compensated images achieving the expected resolution.