Continuity mistake: Just before the fight between Drago and Apollo happens and the announcer is about to announce Drago. Just as the announcer starts saying, "And in the red corner,", we can see Drago in his corner, facing and apparently talking to one of his corner men, indicated by Drago shaking his head yes. Not even a split second later or two words further in the introduction, we now see Drago about 8 feet away from his corner men, pacing as if anticipating to be announced.
Continuity mistake: In round 2 when Rocky hits Drago, Duke his trainer yells 'HE'S CUT' before Rocky even finishes the punch. It's impossible that he would cut that fast, and then a cornerman would see it at the same time.
Continuity mistake: When Rocky defeats Drago, a USA flag that is draped on his shoulders moves from shot to shoot. At first, it is on his shoulders with the stars on the left side. The movie cuts to a different camera and now the stars on over his right shoulder. Then back to the left. Then not visible at all with only stripes on his shoulders.
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.
Factual error: In reality, no referee would ever allow a fighter to basically be beaten to death in a boxing ring. The match would have been stopped after at least one full round of punishment of this magnitude.
Answer: They were Rocky's chaperones. They were even seen in the cabin Rocky was staying in and playing chess with Duke.