When ink is printed on paper, the human eye can't really differentiate dots smaller than about one-six-hundredth of an inch. Possibly those of us with the sharpest eyes might distinguish 800 dots in an inch. Thus, before the era of desktop publishing, low-end photo-typesetting equipment was typically 1000 or 1200 dpi.
Why not just 800 dpi? Well, first there was the margin of error; and second the text being set might need to be enlarged — for instance a headline might need to be larger to fit a particular width — and enlarging any specific resolution lowers the dpi.
(High-end typesetting equipment ran as high as 3000 or 3500 dpi; this enabled gradients or blends to be smoother.
You can't really compare a reflective medium like ink on paper with display media, but display resolution higher than 200 pixels per inch or so is indistinguishable under most conditions. As with print, color gradients or blends will appear smoother with even higher resolutions.
As LCD resolution goes higher than 200 ppi, you probably won't notice any difference in display or normal-sized text. However, text below 6 pts in size does seem sharper.
I haven't done any studies on type color at display resolutions between 200 and 350 ppi, but the higher available resolutions may well benefit bold and italic words within normal text.
So, to summarize: basically 200 ppi display resolution is equivalent to print on better-than-newsprint-quality paper, but variant weights and styles within a single font at the same size may benefit from "retina" displays above 300 ppi.