Major Pearson states that he is employed by the OSS, which was dissolved in 1945- becoming the CIA. The episode is set after that date.
Major Pearson tells the Soviets that they are interested in a man named "Rudolph Abel," who did not adopt that alias until he was arrested in 1957.
Mrs. Dobrenskov says that her husband is "still at the embassy", but he shows up thirty seconds later. Embassies are located only in the host country's capital city, so there are no embassies in New York. Mrs. Dobrenskov should have said "consulate".
One would think that when the police took Rosh Kaleel's finger prints someone might have noticed that his hands and face were very different shades. Makeup in the 1940's came off on everything, Barney Groves (aka: Maj. George Pearson) would not have been able to use white gloves if his hands were covered with makeup.
At about 18:20 as they are talking in the Queen's kitchen, Ellery tells Jenny that Sonja Dobrenskov "was at Colonel Nivin's". But Ellery mispronounces the name as "Neven's"