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Considering persistence-of-vision, rates of 16 fps are normally OK for most people and movies are run at 24 fps. That, however, all refers to actual flashing images, as in movies. From the Wikipedia:

Aside from some configurations used until the early 1990's, computer monitors do not use interlacing. They may sometimes be seen to flicker, often in a brightly lit room, and at close viewing distances. The greater flickering in close-up viewing is due to more of the screen being in the viewer's peripheral vision, which has more sensitivity to flickering. Generally, a refresh rate of 85 Hz or above (as found in most modern CRT monitors) is sufficient to minimize flicker in close viewing, and all recent computer monitors are capable of at least that rate.

Flat-panel liquid crystal display (LCD) monitors do not suffer from flicker even if their refresh rate is 60 Hz or lower. This is because an LCD pixel generates a continuous stream of light as long as that part of the image is supposed to be lit (see also ghosting). With each scan, the monitor determines whether a pixel should be light or dark and changes the state of the pixel accordingly. In a CRT, by comparison, each pixel generates a temporary burst of light, then darkening, in each periodic scan. The monitor activates a phosphor on the screen during each scan if the pixel is supposed to be light, but the phosphor fades before the next scan.[9]

I'd hazard a guess that, all else being equal, it would be coincidental frequency beating that causes the headaches. Perhaps that's not even the cause: my Mrs. had a roaring headache after watching Avatar 3D version - didn't bother me - not a frequency problem at all.