The effect of the tilt is not easy to see on less than full-resolution images (unless you use it to create out-of-focus areas) since it's about sharpness. As for the shift, here are two examples.
In this
autumn scenery photo if shift was not used, the trees on the hill and the reeds would not appear parallel, but those on the sides of the frame would be diverging (leaning towards the frame). In this
redwood forest photo, without shift, the trees would again not be parallel, but appear to be converging. While there is intrinsically nothing wrong with those geometric effects, I feel that they create a distraction that reduces the sense of serenity those scenes inspire. For instance, another
photo of redwoods and rododendrons looking up has a more dynamic character because of the sense of looking up that is emphasized by convergence.
BTW, for full disclosure, those images were photographed with a large format camera, not a T/S lens, but the idea is the same. On such a camera, all lenses just become T/S.