Mark-recapture distance sampling uses detections, non-detections and recorded distances of animals encountered in transect surveys to estimate abundance. However, commonly available distance sampling estimators require that distances to target animals are made without error and that animals are stationary while sampling is being conducted. In practice these requirements are often violated. In this paper, we describe a marginal likelihood framework for estimating abundance from double-observer data that can accommodate movement and measurement error when observations are made consecutively (as with front and rear observers) and when animals are randomly distributed when detected by the first observer. Our framework requires that two observers independently detect and record binned distances to observed animal groups, as we well as a binary indicator for whether animals were moving or not. We then assume that stationary animals are subject to measurement error whereas moving animals are subject to both movement and measurement error. Integrating over unknown animal locations, we construct a marginal likelihood for detection, movement, and measurement error parameters. Estimates of animal abundance are then obtained using a modified Horvitz-Thompson-like estimator. In addition, unmodelled heterogeneity in detection probability can be accommodated through observer dependence parameters. Using simulation, we show that our approach yields low bias compared to approaches that ignore movement and/or measurement error, including in cases where there is considerable detection heterogeneity. We demonstrate our approach using data from a double-observer waterfowl helicopter survey.