The range corrections to the universal properties and structure of two-neutron halo nuclei are investigated within an effective quantum mechanics framework. Treating the nucleus as an effective three-body system, we make a systematic improvement upon previous calculations by calculating the linear range corrections at next-to-leading order. Since the effective ranges for the neutron-core interactions are not known, we estimate the effective range to be set by the inverse of the pion mass. We investigate the possibility of excited Efimov states in two-neutron halo nuclei and calculate their mean square radii to next-to-leading order. We find that the effective range corrections are generally small and the leading order predictions are very robust.