Aberrations, or optical imperfections, exist because no lens is optically perfect. Almost all lenses show aberrations from the ‘perfect’ image.
Corner shading is another term for 'vignetting', where the corners or the edges of a picture look darker than the center. This is a common phenomenon with lenses, though today's lens designers work hard to eliminate it. Some photographers feel it can add to the 'look' of an image, however.