Factual error: In the very beginning of the movie broadcasters around the world are commenting on the mysterious spaceship. To lend a bit of calm and normalcy one broadcaster notes that despite what is happening many people are enjoying the fine spring weather in the Capital, to this end picnics and the wonderful cherry blossoms are plainly depicted. Shortly afterward when Klatu leaves the hospital, he is seen examining the cleaner's tag on the suit he "borrowed". This is where he adopted the name Carpenter. Clearly printed at the top of this tag is the date 7/18 1951, not spring by at least a few months.
Factual error: The scientists are supposed to be at or near the North Pole. When Capt. Hendry takes off from Anchorage, Alaska the sky is dark (day-for-night) but when he arrives at the Polar base it is broad daylight. The dialogue says the date is Nov. 2 (presumably 1951). Later, when the "Martian" is accidentally released from his block of ice by an electric blanket, the sky is dark again. Later the sun is back up. At the North Pole the sun sets around Sept. 21 and stays down until March 21, when it comes back up. NOAA says polar twilight lingers through "early October" but by November the sky is black 24 hours a day and stays like that for most of the next six months. Also, when he arrives Capt. Hendry is told the explosion took place about 50 miles "due East." If you're at the North Pole there's no such direction as "due East". No matter which way you head, you're heading due South. And from the plane, Hendry refers to "that peak ahead" being due East. The Arctic ice cap is a thick sheet of ice floating in the ocean. That's why submarines can sail underneath it. There are no "peaks" near the North Pole. These guys were thinking of Alaska, not the North Pole.
Factual error: When the messenger has given the photos and materials to the doctor, the data is given to 'DA' or differential analyzer (just like in earth vs the flying saucers). What is shown is a standard card sorter which does nothing but put cards in order. This machine then outputs its info to a standard plotter which can only produce x-y diagrams. It would be easier to do the verification calculations by hand using a slide rule and some graph paper.