Lens Reviews tested this lens and found some interesting results, see here.
The main point is near the bottom,
The 18-105mm does show some evidence of
corner shading, but its presence is fairly subtle. If you demand
absolutely no corner shading in images produced by this lens, you'll
have to use it at apertures of ƒ/11 or smaller; larger apertures
result in some form of corner shading. Using a focal length of 35-50mm
will help; these focal lengths are a bit more forgiving, and will only
produce significant corner shading when the lens is used at apertures
wider than ƒ/8.
At the focal length extremes, upwards of 2/3 of a stop of corner
shading can be seen when the lens is used at its largest aperture.
and also here
If there's a weakness in the lens at all, it would be performance at
105mm, where image sharpness doesn't quite reach the level seen at
other focal lengths. However you'd be hard-pressed to see the quality
difference in practical use.
The lens received high praise over all from the reviewer, but did state the same issues you discussed.