My calculations:
degrees in one inch - arcsin(1/12) = 4.78
Pixels in eye for one inch, 12" away - 4.78 * 50 = 240
Same calculations for 10" arcsin(1/10)*5 = 287
I think something is wrong with the numbers in the article
If your eye can resolve 50 cycles per degree, that means it can tell the difference between a uniform grey and something that alternates between black and white 50 times per degree. To display such a pattern, you'd need 100 pixels per degree (black, white, black, white, ..., with 50 pairs).
So I think Soneira guy is off base. But I think the much bigger problem is that both Soneira and the 1 minute definition are talking about the acuity of a 'normal' person, and seem to be largely ignoring the issue of a significant variation in the population. My question is, for what portion of the population does this display exceed the limits of their visual acuity?
On the other hand, elsewhere Wikipedia says that it means being able to distinguish Snellen optotypes whose total size is one arc-minute. On the face of it, that implies more resolution than two pixels per arc-minute. (Hand-wavily, maybe it's about the same: if you can resolve 2x2 pixels in a square of side 1 arcminute, then for high-contrast Snellen-type images that maybe suggests that you ought to be able to distinguish about 2^(2x2) = 16 different such images, and a Snellen chart actually uses 10 or 12 different optotypes, depending on whether it's one of Snellen's original ones or a modern variant. That's pretty close to 16.)
Phil Plait's blog entry that someone else linked to talks about the difference between "normal" and "ideal", and concludes that an average person looking at a new iPhone at 1' distance will indeed not be able to resolve the pixels (though not by much).
So yeah, if you drew out a tiny "E" (or "P" or "F", I don't think it matters) on a 326 ppi screen a bit more than 12 inches from the viewer's eyes, where the width of each bar was 1 pixel and the space between bars was 1 pixel, then I think that would match up closely with the standard for normal vision, at least in terms of visual acuity for one eye.
Matching that up with the resolution of a display device is still a bit subtle. For instance, suppose you're trying to display an "E" of that size on the display, but it's offset by half a pixel vertically. Result: you get a grey rectangle that's a bit darker along the left edge. :-)
(I think my conclusion from all this is: what Apple are claiming about the iPhone 4 display is about as close to the truth as it's reasonable to expect in marketing materials. That is: everything they've said is at least defensible, but they've put a very positive spin on everything. Seems fair enough to me. And as a pixel-freak who isn't currently a smartphone user, I'm awfully tempted by the new iPhone...)
Degrees in one inch - arctan(1/24)2 = 4.77 "Data points" in eye for one inch, 12" away: 4.7750*2 = 477 (magic number cited in article)
Why the last multiplication by 2? The eye doesn't see pixels, it sees color difference, which means that the limit (not the minimum) is when two of those pixels cover the same "cycle" -> 1 color change in the cycle (in any case, that's how I understood the article).