Factual error: When Bruno is on his way to Union Station, he's heading on a bridge away from the Lincoln Memorial, which means he's leaving Washington D.C. for Arlington, Virginia, or in other words, he's going the wrong way.
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: 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.
Factual error: When the Reindeer aircraft is on the ground at Gander, Jimmy Stewart pulls the landing gear handle, but only the left main gear folds up. All three landing gear (left, right, and nose) would have folded together.