Revealing mistake: As Forrester is easing up to check the Martian arm, a second Martian flyer crashes. As it does, you can tell that it is a re-use of the first one crashing, but flipped so that it's hitting left side first rather than right side first.
Character mistake: During the first big battle between the Martians & the U.S. Army, the Martians use their heat ray to vaporise people and equipment. Dr. Forrester, a physicist, then quickly speculates, "It neutralises mesons somehow. They're the atomic glue holding matter together. Cut across their magnetic lines of force and any object will simply cease to exist." During the '50s mesons were theorised to hold atomic nuclei together strongly. But if the Martian rays worked as the Dr. guessed, then objects wouldn't just vaporise. They'd explode with the ferocity of nuclear weapons.
Revealing mistake: When the military starts firing, not only do you see the wires holding the saucers, but the "electromagnetic shields" can be seen as glass or plastic domes, as the studio lighting is reflecting in them.