Revealing mistake: Rocky, Apollo, Adrian, and Paulie are filmed from behind walking to Apollo's gym (notice Rocky and Apollo are the same height). When Rocky turns to walk in the door, you see heels at least three inches tall on his feet.
Character mistake: During Mickey's MI it's stated that his blood pressure is 200/50 (that alone is ridiculous) and the doctor immediately says "OK. Let's start CPR." If Mickey has a BP he has a pulse, and any CPR certified healthcare provider would know that you can't do CPR on a patient with a pulse.
Revealing mistake: During the movie's opening title sequence, Clubber Lang knocks out Jaffe in the sixth round. If you watch carefully, you can see that Lang's boxing glove actually hits Jaffe's shoulder, but he still knocks him out in the process.
Continuity mistake: When Rocky leaves the Jewish mausoleum on his motorcycle, he has no helmet. When Rocky arrives at his statue, he is now wearing a helmet.
Suggested correction: So he stopped either at home or a store and got a helmet.
Revealing mistake: When Paulie throws the bottle at the Rocky pinball machine at the beginning of the movie, the glass smashes but the bottle doesn't, indicating that the bottle is an obvious prop.
Suggested correction: Liquor bottles are small and dense and much stronger against damage than a thin sheet of plate glass.
Revealing mistake: Look closely after Thunderlips powerslams Rocky. Mainly when he pulls him up by the hair. Clearly that's not Sylvester Stallone but a stunt double.
Factual error: After the match with Thunderlips the newspaper says it was Wednesday, May 15 1982, but that day was a Saturday.
Continuity mistake: After the first match with Clubber, Mickey gets sick and Adrien makes a pillow with her coat for him. Just before he lies down his hat disappears.
Revealing mistake: In a shot of Clubber Lang and his manager standing in the corner at the end of the first round during the rematch between Lang and Rocky, "Clubber" on Lang's boxing shorts and "Heavyweight Champ" on the manager's shirt are back to front, indicating that it is a reversed shot.
Continuity mistake: When Rocky is choking Thunderlips he does with his left arm, then after an angle change it's his right.
Visible crew/equipment: During the second fight, there's a brief shot looking at the opposite side of the ring. A large motion picture camera and its operator are blatantly visible in the crowd.