Factual error: The limos they are driving in Russia are American Mercedes Benz models (American style bigger bumpers and headlights). Very unlikely at that time.
Factual error: Drago is presented as an infantry Captain in the Soviet Army. However, during the press conference his shoulder bars are the same as a soviet Colonel, not a Captain.
Factual error: During the press conference scene, Drago's hat should have an officer's gold cap cord, but instead has only a black chinstrap, which, combined with that style of cockade means that the cap is only approved for wear by warrant officers in the Soviet Army.