TV screens have higher persistence phosphor than monitors, as you can easily see if you press a torch to the front of a turned-off TV in a darkened room, give it a burst of light, then observe the faintly glowing circle it leaves. Monitors do the same thing, but fade faster. You need a 75Hz or better refresh rate to eliminate the flicker. This, combined with the higher persistence phosphor, gives a decently flicker-free display. And, of course, you usually watch TV from far enough away that the screen takes up less of your field of view than does your closely-viewed computer monitor.
Smaller images seem to flicker less.
24 frame per second movies, on the other hand, get away with their low frame rate without looking painfully flickery because the whole frame's illuminated in one go each time. And LCD panels work the same way. There's no scanning dot on an LCD - each subpixel just has its own little transistor, which turns on when it's needed to and stays that way until it's told to turn off. There's no inter-frame fading, because there aren't really any frames, as such. Many LCD monitors will run from signals with a range of refresh rates, but it's just a convenience feature - there's no perceptible difference in the image on the screen.