Just Plane Wrong: Although the film treats looping a helicopter as aerodynamically impossible, this is not actually the case. It depends more on the performance characteristics of the aircraft in question than an absolute rule of physics.
What Could Have Been: The original concept for the film was something along the lines of Taxi Driver in the air: Murphy was to have been a police helicopter pilot who went on a psychotic rampage through the skies of LA. This gets reused as the cover story for why the police and Air Force want to shoot him down.