At the end of the Drago/Rocky Bout... Rocky gives a speech where he says, "Today there are 2 people killing each other but I guess it's better than 20 Million people". The Russian translator however translates this as "It's better than 20 Million Dollars".
When Rocky first arrives in Russia, Paulie can be heard complaining about the conditions in which he will have to live in. He references not being able to watch the Rose Bowl game out here; however, the Rose Bowl game is not played until New Year's Day. Rocky's fight takes place on Christmas.
Before the fight with Creed and Drago, just after the James Brown dance sequence, Creed points at Drago without gloves on, telling him he is going down. Then in the next shot, Creed has his boxing gloves on.
In the Creed/Drago match, Rocky picks up the towel and holds it high in his left hand, cocked ready to throw. As the scene switches between the close-up on Rocky and Drago punching Creed, you can clearly see Rocky in the background in his white "BOSS" sweatshirt casually holding the towel at his side, away from the corner. The shot goes back to Rocky at the corner with the towel high and then back to the fighters. Rocky is again seen in the background with the towel low by his side away from the corner.
When Rocky is driving and thinking about Drago, there is a flashback to the Drago/Apollo fight, but one of the shots of Drago is actually taken from the upcoming Rocky/Drago fight, because the trunks are the wrong color and Drago is bleeding
In a brief scene, while Rocky is training for the big fight with Drago, Rocky is punching the punch mitts that Tony Duke is holding in the air. In one shot, Rocky is punching the punch mitts with black boxing gloves, and in the very next shot, Rocky is punching the punch mitts with white tape, no gloves.
During the end of the 14th round, it can be clearly seen that Drago has thrown Rocky and is punching him in Rocky's corner. When the bell goes and the respective teams storm into the ring to split them up, it can be clearly seen that they are now in Dragos corner, with the red ring post behind them as opposed from the white.
During the montage, whilst Rocky is driving around reminiscing about the past, there is a clip of Rocky and Apollo jogging in front of a mirror. At the bottom of the mirror you can see a small camera light moving back and forth.
Throughout Rocky's training in the wilds of the USSR he is frequently filmed with the Tetons and the Grand Teton in particular in the background. Only notable because of how identifiable and unique the Teton range is.
After the Creed/Drago match, when there is a montage of newspaper clippings about Rocky deciding to fight Drago, the first clipping if you look closely at the article and read it... you'll notice that the article isn't even about Rocky, but that it is actually about the world series.
When Apollo announces his intention to fight Drago before the press, a montage of newspaper clippings is shown just before this. The print of one of the articles, with photos of both Apollo and Drago, doesn't report the upcoming fight at all but instead is about union-employer negotiations at the Chrysler company.