In the pan shot of the Pan American dockside terminal when Diane Palmer is boarding the Orient Clipper you can clearly see a modern window-style air conditioning unit sticking through the front wall of the terminal building. Such units did not exist in the time period in which this movie was set (late 1930s).
When the Phantom has hijacked the plane after his daring rescue operation, the captors fire bullets at the plane, hitting the wing and causing leaks. However in the shot following it, the wing shows no sign of damage.
When the Phantom climbed through the elevator shaft as the elevator was descending upon him, he clearly went through on his stomach and then his legs.
Then, from the other side he appears that he was on his back and then rolled upward to stand up. The positioning changed as he went through the shaft and is not consistent.
The float plane used to take Drax from New York City to the Devils Vortex (somewhere off the Malay Peninsula) is a Beechcraft Model 18. The range of this aircraft is 1200 miles. The plane could not fly the approximately 10,000 miles without stopping to refuel at which point the Phantom would most likely have been seen hanging onto the float by someone.
Even if the plane could have made the full flight non-stop, with its top speed of 225 MPH, the Phantom would have had to hang on to the pontoon spar for nearly 2 days.
The Martin M-130 "Clipper" aircraft depicted in the movie never existed. Only 3 were built, all flew for Pan American, and were named "Hawaii Clipper", "China Clipper", and "Philippine Clipper". The aircraft in the movie is named "Orient Clipper". None of the 3 M-130s survived WW II.
A horse cannot gallop fast enough to overtake an airplane. Since the men could not see the airplane while riding through the forest, it is unlikely that they would arrive at the exact spot where the airplane crashed.