What differences might a brain discriminate between natural pigments and JPEG copies of those same 'hues' on a screen. Or what difference the particular type of screen -plasma or lcd or analog might also make?

the colour palatte of computer screens does not cover the whole gamut of colour that our eyes can detect. that would be one anyway. it covers most of it though so the answer would be 'damn few'

What about image 'compression', using JPEG or MPEG which discards certain visual information, which the algorithm decides isn't important. This possibly applies to MP3 too, because it does a similar thing with sound. JPEG, MPEG and so on are 'lossy' algorithms, so does it affect our perception at all?