I've read that there will be a space elevator in the new movie. As we all know such a structure isn't going to last long given the general chaos that goes on in AC so (we all know what happened to their "super computer in space" right? :P )...
If the space elevator gets destroyed I do hope it falls up and not down otherwise they will be making a big physics mistake.
My knowledge of space elevator physics may be rusty but from the types of space elevator's I'm aware of, the centrifugal force of the Earth's spin is what is supposed to keep a space elevator aloft. Theoretically you could simply build a rigid structure to go that high but it would be impractical. Probably even by Academy City standards.
But it all depends on how it gets blown up/damaged or whatnot. If it's destroyed at the base, then the whole thing will likely just fly up into orbit and will be rather uneventful for those on the ground unless there's a little "whiplash" in the cord like material that they end up using as the tether for the elevator and it happens to strike a nearby building or something on it's way up. :P
If in the unlikely event they use a ridged structure to "hold" it up, then of coarse the entire thing will just fall to the ground since most likely it won't be built at the right hight for any significant portion of it to fly up through centrifugal force.
However, if the top of the elevator gets blown up, then that would be the only instance I can think of where 90% of the entire structure could fall back to earth. The material holding it to the ground must be light but strong. Thus the structure they have on top must be heavy and have enough mass so that the spin of the earth can keep proper tension on the cord or whatever material they chose to build it with. So if the top gets yanked off, gravity takes the cord back down since that mass is no longer "pulling" it up. The rules on taking down a tower would work in reverse for a space elevator. To make it fall to earth you destroy the top and not the bottom. :P
A proper space elevator held in place by a light corded type material (like nano-tubes of some kind or some other super light material) that would have a permanent mass on top to act as the ballast, The elevator it self (the part that moves up and down) must always have less mass and less mass in it then that ballast otherwise it will be pulled down via gravity and the structure will fail. Thus "pulling" it down is another viable way of destroying it and having it fall to Earth.
Something Accelerator might try if he happens to be the one to destroy it. You wouldn't have to pull it very far either. Just enough where it gets too low for the centrifugal force to keep it up and then gravity would just do the rest of the work. Unless Accelerator is in a hurry to get it down. :P
I will be very interested to see how they chose to render this elevator. I have not seen a single show or movie that features this technology, so it will be interesting.
Another thing would be to see how they handle what goes on in the elevator when it's at the very top in space. Logically they should place it high enough so that people on the top would feel the centrifugal force and be pulled to the ceiling in a "artificial gravity" sort of way. That way it could be useful for extended stays without the usual high orbit health issues you get for staying in zero g for so long.
If they want to do any micro gravity/zero gravity experiments, they can simply lower the elevator down to a height of their choosing. They could then simulate varying degrees of gravity. Mars gravity, moon gravity or zero gravity. One of the perks of having a space elevator. :P
Also the elevator will have a cargo limit. They can't put more stuff in it then what the ballast on top weighs. But one could simply send up smaller objects to add on to that ballast should they decide to "upgrade" it's cargo limit in the future. That and the strength of the material holding it to Earth is the ultimate limit.