Factual error: When the alien craft speeds away from the NASA base, its slipstream tears off the roof of a small booth. But the wake also should sweep the people in its flight path down to the ground; it is too close for that not to happen.
Factual error: After David's ship breaks free and exits the hangar, he orders Max to take him 20 miles away. Back at the tracking room a technician informs Dr. Faraday that the ship has gone 20 miles straight up, but the target altitude indicated on the screen reads 184,800 feet - more than a 35 mile distance. (00:52:00)