Sometimes with some fabrics there can be less moire in 16 bit as well as less purple fringing.
and yes most people won't notice it. However by the time its gone through a few processes and printed up nice and large in a quality catalogue or magazine or even as one of those 'super zoom' features popular on websites now then it may become more visiable to which I've known non photographers to just note that the 'image doesn't look very professionally polished'
Conversely though unless the image is a really high end image in the first place again its less likely to be seen, i.e. not lit or focused properly, using a lower end camera and / or lens. The images are lacking all that extra detail. (not to be confused with sharpness)
I'd recommend ALWAYS editing in 16 bit, regardless of what your output format is. This will allow effects such as curve modifications and layer blending to retain a level of tonal 'smoothness' that 8-bit simply cannot deliver.
On a good monitor I can see the differences in tone on 8-bit and I'd wager others could too, especially with things like flatly lit walls in images. Also JPG compression can cause artifacts with flat areas of colour, something to think about if uploading files for print as JPG (rather than something with lossless compression like TIFF/PNG).