I remember the Liberian Star (circa 1964) and its mixed fonts without fondness (I think they used one set of letter bins for headlines and another set for text body, regardless of size): I prefer the simplicity of having a single font on the page. It does make the page easier to read.
However. Suppose one allowed a tiny amount of "hair" in the font--the length of the serif, its exact angle, that sort of thing. Not so much that it wouldn't be obviously the same letter from the same font, but enough that the eye could catch the difference. There might be 5 very close versions of the letter t, which the display engine uses alternately in the body of the text.
Would that make the sea of letters less uniform, and easier to navigate?
Creating a new font for this sort of thing would be pretty easy (creating a good one is quite a bit harder!); the hairy part is the display engine that picks which version of k to use. A unicode test page wouldn't be too hard for a pro to whip up, but it would probably take a pro to evaluate it quickly--otherwise you'd need a lot of pages and a lot of amateur eyeballs. I don't know what to look for: I only tend to notice that I get tired reading something, and not notice the fonts or lighting.
UPDATE: See Grey-Text for another description of the problem.