I really usually don't look for movie mistakes, but in Indy's case I have started to think about one right at the cinema:
Colonel Doctor Irina Spalko, the "Stalin's favourite person, award holder of the Order of Lenin, the highest decoration in the Soviet Union, three times for outstanding services rendered to the State, and the honorary title of Hero of Socialist Labor for exceptional achievements in the national economy and culture" just could not be the "Stalin's fair-haired girl" because:
1) This Indys case is situated to the year of 1957. Stalin died in 1953.
2) If she had been "Stalin's fair-haired girl" in his days, she probably had not boasted about it in 1957. This is one year after the Khrushchev attacks the veneration of Stalin as a "cult of personality" and Stalin already wasn't as venerated as before.
3) No one intelligent boast to be a Stalin's favourite.
Two links about Irina Spalko: