When the engine on the plane fails, the prop, as seen from inside the plane, is tilted towards the fuselage. But, as seen from the outside, it is tilted away from the fuselage.
Mark Bradley claims Dr. Paul Lujan "worked with Dr. Einstein" on the development of the atomic bomb, but Einstein did not work on this project. His only involvement was a letter to President Roosevelt in 1939 warning that the Germans had an atomic bomb program and advising the U.S. to begin its own research, as well as the theoretical work he completed decades earlier that allowed scientists to calculate the amount of energy such a bomb would produce (via his famous equation). Einstein himself said the idea of an atomic bomb had never even occurred to him until Hungarian physicist Leo Szilard came to him with news of the German effort.
The island seen through the plane's windows before it crash lands is clearly not the same as the "island" they land on. The real island seen from the plane is a large, steep mountain jutting up from the ocean, quite obviously without the beaches, jungles, lagoon or flat lands depicted in the rest of the film.
The footage of the B-29 Superfortress show has been flipped, as can be seen by the plane's serial number on the tail and under the wing.
The starboard (right) engine quits and Joe exclaims "there goes number one". Aircraft engines are numbered left to right as the pilot sits facing forward, so it was engine number two that failed.