Centroid positions of peaks identified in weak-lensing mass maps often show offsets with respect to other means of identifying halo centres, such as position of the brightest cluster galaxy or X-ray emission centroid. Here we study the effect of projected large-scale structure (LSS), smoothing of mass maps, and shape noise on the weak-lensing peak positions. In addition, we compare the offsets in mass maps to those found in parametric model fits. Using ray-tracing simulations through the Millennium Run N-body simulation, we find that projected LSS does not alter the weak-lensing peak position within the limits of our simulations’ spatial resolution, which exceeds the typical resolution of weak-lensing maps. We conclude that projected LSS, although a major contaminant for weak-lensing mass estimates, is not a source of confusion for identifying halo centres. The typically reported offsets in the literature are caused by a combination of shape noise and smoothing alone. This is true for centroid positions derived both from mass maps and model fits.