We present results of an atomic-scale study on in situ cleaved InAs(110) in the dynamic mode of scanning force microscopy (SFM) at low temperatures. On a defect-free surface, the dynamic mode SFM images always exhibit strong maxima above the positions of the As atoms, where the total valence charge density has its maximum. Occasionally, with certain tips, the In atoms also become visible. However, their appearance strongly depends on the specific tip-sample interaction: We observed protrusions as well as depressions at the position of the In atoms. In this context, the role of the charge rearrangements induced by the specific electronic structure of the tip on the contrast in atomic-scale images is discussed in detail. Additionally, we investigated the appearance and nature of two different types of atomically resolved point defects. The most frequently observed point defect manifests itself as a missing protrusion, indicating the existence of an As vacancy. A second type of point defect is probably an In vacancy, which could be detected indirectly by its influence on the two neighboring As atoms at the surface. At large lip-sample distances, these As atoms show a reduced corrugation compared to the surrounding lattice, while at smaller tip-sample distances the corrugation is increased. This distance-dependent contrast inversion is explained by a relaxation of the As atoms above the defect which is induced by an attractive tip-sample interaction.