We demonstrate that in random-stacking hard-sphere colloidal crystals the stacking disorder not only exists in the direction perpendicular to the close-packed layers, but also extends in the lateral direction. The existence of such in-plane stacking disorder is suggested by a recent observation of lateral broadening of the Bragg scattering rods in microradian X-ray diffraction and is further confirmed here by real-space confocal microscopy in two hard-sphere colloidal systems with different relative gravity effects. Due to the in-plane stacking disorder, the hexagonal planes consist of islands with different lateral A, B, and C positions with characteristic line defects in between them. The real-space layer-by-layer stacks of images also reveal the 3-D structure of the defects. The chance zeta to find another line-defect above a line-defect in the layer below turns out to be close to 1/2independent of relative gravitywhich can be explained by the two different stacking options above a defect. The stacking of a few sets of several line defects situated on top of each other turns out to be predominantly FCC-like.