Continuity mistake: In the laboratory, the lenses of the Martian camera were tilted in the frame in the closeup, then righted in the wide shot.
Other mistake: When the Martians first land on earth, the ship is so hot, it starts fires in the surrounding area, and can't be approached for hours later. Yet later, when another ship crashes directly into the farmhouse, there are no fires, and the farmhouse certainly doesn't catch fire.
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.