Three-dimensional (3D) localization-based super-resolution microscopy (SR) requires correction of aberrations to accurately represent 3D structure. Here we show how a depth-dependent lateral shift in the apparent position of a fluorescent point source, which we term 'wobble', results in warped 3D SR images and provide a software tool to correct this distortion. This system-specific, lateral shift is typically > 80 nm across an axial range of similar to 1 mu m. A theoretical analysis based on phase retrieval data from our microscope suggests that the wobble is caused by non-rotationally symmetric phase and amplitude aberrations in the microscope's pupil function. We then apply our correction to the bacterial cytoskeletal protein FtsZ in live bacteria and demonstrate that the corrected data more accurately represent the true shape of this vertically-oriented ring-like structure. We also include this correction method in a registration procedure for dual-color, 3D SR data and show that it improves target registration error (TRE) at the axial limits over an imaging depth of 1 mu m, yielding TRE values of < 20 nm. This work highlights the importance of correcting aberrations in 3D SR to achieve high fidelity between the measurements and the sample.