Madeleine says to her father Pug that Pamela's fiance, Lord Burne-Wilke, is a "blond dreamboat," but when we see him with Pamela later in the episode, the actor playing him has dark brown hair.
Personnel in German bunker at the end of the Stalingrad battle are carrying Panzerfaust anti-tank rockets (January 1943). In reality, these didn't exist until October 1943.
Breckenridge Long has a photograph of Franklin Delano Roosevelt in his office, and it is clearly a picture of the real FDR, not Ralph Bellamy.