The model used for the crash sequence cost $250,000 and was so perfectly built it actually flew further than the crew and testing had predicted. In fact it flew so far it hit the camera filming it and broke the cameraman's leg.
The production built a "Phoenix" that could be taxied, but were unable to safely build a flying version economically. Mindful of the original production which did build a "Phoenix" that could fly, but was structurally unsound and crashed killing stuntman Paul Mantz, the flying scenes were done using a radio controlled model and computer graphics.
Miranda Otto's character, an engineer, is named "Kelly Johnson". Kelly Johnson is the name of a legendary aircraft engineer for Lockheed who designed the P-388 Lightning fighter of WWII. Later he ran the Lockheed "Skunk Works" which secretly produced the U-2 and SR-71 spy planes. In view of the fact that aircraft design is a key element of the plot, it is unlikely that the name is a coincidence.
The production transported three C-119 fuselages to Namibia where the film was shot. During transportation, a ferry carrying the fuselage and its trailer across a river sank and the parts had to be salvaged.