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".
During the First 2 Rounds of the Rocky/Drago Fight the USA Announcers are seen on the side of the ring right in front of the Fighters. The Main Commentator is talking during the fight but if you look at the quick shots of the commentator that should be talking his mouth is not moving.
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.
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
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.
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.
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.
When Rocky returns home from his "favor" for Apollo and his son is filming, Rocky's right eye is black. In fact, in the "favor" fight, Apollo throws a right while Rocky throws a left. Rocky's head and chin are tucked down slightly to his right which would make it impossible for Apollo's punch to hit him in the right eye.
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. Given that the film was shot during the Cold War, it would have been very difficult, if not impossible, for a film which is basically about the Cold War and the Russians losing, to be filmed in the USSR.
At the end of the fight, Rocky makes his speech, then says "Hello to his kid at home who should be sleeping" And seen in the background of the house is a window that is black due to night time. However, Moscow (where the fight is being fought) is 8 hours ahead of New York. Thus, even if the fight ends at Midnight Moscow time, it's still 4pm New York time and even on Christmas Day, the sun is still up at 4pm, And his son would have no reason to have to be in bed sleeping.
The high-ranking Soviet officials who visit Rocky arrive in a black Mercedes limo. Officials in communist Soviet Union would never use a Mercedes because it is a symbol of Western economic might. They would use one of the Soviet-made Zil limos that communist party officials used at the time.
When Dragos' Manager is yelling in Russian at Dragos' corner man, the caption reads " You trained this fool, he's a disgrace." If you listen carefully he is actually speaking english, and he says " This stupid jerk is unbelievable, he is nuts."
Rocky gets the worst beating of the entire series in this film. However, he doesn't have nearly the extent of facial damage that he received in the first two Rockys. In Rocky II, his face was literally beaten to a pulp. Here, his injuries are very minor by comparison.
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.