Revealing mistake: At the beginning of the HBO broadcast, some brief clips of Mason "The Line" Dixon in action are shown. Look closely at one clip where he's wearing white trunks, and you'll see "TARVER" written across the front in big black letters, revealing, of course, that it's a real-life clip of boxer/actor Antonio Tarver.
Continuity mistake: After the final fight Rocky is walking to the dressing room and waving to the fans. He then stops and hugs Spider, then Marie and her son and then Duke and they walk off. The camera then goes back into the ring where they announce Dixon has won. But in the bottom left of the screen you can see Duke still in the ring but he had already left and had gone back into the dressing room.
Factual error: The three scorecards of 95-94 for the Dixon vs Balboa fight could not possibly be scored that way for a ten-round professional fight in which so many knockdowns occurred. Each fighter went down multiple times, which would've resulted in a much lower set of numbers using the ten-point-must system enforced in Nevada (and pretty much everywhere else).
Character mistake: In the scene where Spider quotes from the Bible to Rocky before the fight, he quotes the verse as Zechariah 4:6 and then quotes the beginning of that verse but the end of another verse, 1st Corinthians 15:57.