I have worked in aspects of the motion picture industry for almost 30 years, and IME, high frame rates in motion pictures are perceived differently from refresh rates of CRT video screens.
Like other posters here, I can see a bit of a flicker on computer monitors at rates below about 70 cycles. On the other hand, I’ve seen 60 fps motion pictures (i.e. Showscan) and did not have the impression of a flicker, nor do I with regular movies, which as Exapno pointed out, are shot at 24 frames per second, but projected at 48 flashes per second. This no doubt has to do with the different ways in which the two methods operate.
However, other effects are noticeable in motion pictures, particularly to directors and other expert observers. Specifically, strobing, which is most obvious to ordinary viewers in the case of wheels appearing to move backwards, but also happens with many other forms of motion. Strobing is caused or exacerbated by the repeating of each frame twice, and happens when motions of objects across the screen (or the entire image in the case of pans) are so large that they appear discontinuous. It’s a sort of jerkiness that many people don’t notice consciously, but which can become painfully obvious in poorly shot scenes, once you’ve become aware of it.
Strobing is especially noticeable on larger screens, as in IMAX theaters, my particular field. As a result, IMAX filmmakers take special precautions to control their camera motions to avoid strobing.
Raising the frame rate (as opposed to the flash rate) reduces strobing, because even in fast moving scenes the jump between successive frames is relatively small.
Special effects wiz Douglas Trumbull, experimented with many high frame rates before settling on 60 fps for the Showscan system he invented. He told me that some strobing effects that were still visible at 60 fps were pretty much gone somewhere between 70 and 80 fps. He would have liked to run Showscan at 72 fps, but there were too many advantages to 60 fps: since it’s the same frequency as U.S. mains power, it’s easier to run motors and other components at that rate. Also, it matches perfectly with HDTV.
(FYI, Showscan and other film systems that run above 30 fps flash each frame only once.)