William Moulton Marston was portrayed as a spy and in one brief scene reminisces about his military service and things he had seen. However, he received his commission as a 2nd LT on October 22, 1918 just 20 days before the end of World War I. He was stationed at Fort Oglethorpe GA, Camp Upton NY and Fort Lee VA before being discharged on May 19, 1919. Despite his portrayal in the movie, Marston never left the US and never saw the war first hand. Source: Harvard's Military Record in the Great War (1921).
A major scene early in the movie takes place in a Radcliffe College sorority. Radcliffe, which was later absorbed into Harvard University, never had sororities. Harvard has had fraternities. Theodore Roosevelt, for one, was in a fraternity at Harvard. Also, in, e.g., The Social Network, they discuss a Jewish fraternity at Harvard.
When the professor was in the hospital at the end of his life his room had modern features that would not have been in hospital in the 1940's. These include a sprinkler system, modern electrical boxes and some large, modern A/C units outside the windows.