I'd have to research, but I don't think LCDs refresh, per se, as the cystals are always excited. Someone with more knowledge will have to help me here.
As for movies, yes they're shot at 24. I am shocked at how often this fact is used to try to prove that you "only need 24". 24 is actually just about the bare minimum. IMAX movies are shot at 48 frames per second at great expense! I don't think they'd do it if you couldn't tell the difference.
The human eye can easily see the difference in framerate between 24 and 30 and some people can see the difference between 60 and 80. I'd say 75-80 is the limit of human perception.
I know when I have my monitor refresh set to 60 Hz, I get a headache.