An elevator falling through a hole drilled all the way through the Earth would quickly reach terminal velocity due to aerodynamic drag.
Gradually, the elevator's velocity would grow smaller, as gravity grew weaker (gravity is zero at the Earth's center). The elevator would thus coast to a stop near the center of the Earth, with no means of getting back out (apart from a 4,000-mile cable pulling it back up).
Even if you evacuated the tube so there would be no air resistance, you would still collide with the walls (at incredible speed) due to the Earth's rotation. Any attempt to keep the elevator on track using rails would only add friction, making it impossible to reclaim the altitude from which the elevator was initially dropped.
I don't know what this show was about, but if it claimed you could get from one side of the Earth to the other in 40 minutes by falling through the center, it is sorely mistaken.