The Movie: The Enterprise sustains hardcore damage and the power system fails, hurtling the ship towards Earth. Whatever system is in charge of the ship's artificial gravity is out, causing it shift orientations in rapid succession. Our heroes stumble about grabbing on to stuff so they don't tumble to their deaths when the next shift takes place.
Real Life: Unless an object approaches Earth at an extreme velocity, like the comet that wiped out the dinosaurs, Earth's gravitational field will pull the offender into orbit around it, not directly towards it. That's just the nifty way these fields work, and it's why we orbit the sun instead of falling into it. Also, the shifting orientation of gravity inside the ship makes for some great action, but the human body really can't stand that kind of gravitational instability. The vestibular system in the brain helps orient us in space, but it would essentially overheat in this situation. The crew of the Enterprise wouldn't have a choice about falling — they'd have lost consciousness after the first few gravitational realignments.