Revealing mistake: Take a good look at the lower right corner during the 'Hearts on Fire' training sequence at a barn in Russia. Rocky does a few leaning sit-ups; at that moment the cow in the lower right corner moves backwards. When you look closely you'll see it moves back too quickly and anatomically incorrectly, thus revealing it's a fake head attached to wheels or something. (00:57:45)
Revealing mistake: As you watch Rocky fight the Russian, watch closely during round three. In a couple of punches, you can see that Drago does not make contact with Rocky, but the sound effects and Rocky's movements indicates that Drago hits him hard. (01:13:45)
Revealing mistake: When the newspaper articles are being shown, the newspaper article is headlined "Rocky vs Drago - for Guilt or Glory". The actual article is talking about the Kansas City Royals playing in the World Series, which has nothing to do with Rocky vs Drago. (00:17:00)
Revealing mistake: As Rocky backs up his car at the beginning of the montage scene after the press conference with Drago, you can see the "bricks" buckle under the weight of the car signifying that they are fake. (00:41:30)
Answer: They were Rocky's chaperones. They were even seen in the cabin Rocky was staying in and playing chess with Duke.