The recently proposed third-order Douglas-Kroll method (DK3) is applied to superheavy element 112, the hydride of 112, and its ions. The results are compared to the second-order DK (DK2) results. The effect of the third-order scalar relativistic corrections with the DK3 Hamiltonian is found to be relatively small for the valence-shell properties of element 112, (112)H, and its ions although DK3 represents a significant improvement over DK2 for the inner core shells.