When the Family is departing for the camps by train, An Announcement uses the Phonetic Alphabet BRAVO for B when referring to the train. BRAVO is the Current Phonetic Alphabet but during WW2 it would have been BAKER. ABLE BAKER CHARLIE, not the current ALFA BRAVO CHARLIE.
Toward the end when Lily is sitting at the kitchen table she reports to her aunt that a big bomb, an atomic bomb, was dropped over Hiroshima. "In a 1/10th of a second 200,000 people were killed". This is a factual error. Approximately 70,000 were killed that day and roughly another 70,000 by the end of 1945.
During the destroying Japanese businesses scene, the "I am an American" sign is printed as if from a professional printers, however, it's entirely possible that people had signs professionally printed.