Other mistake: Rocky says "cut my eye" during the fight scene, if you watch closly you can see the man actually squeeze a tube full of red stuff inches away from his eye. It's really quite funny...
Revealing mistake: At the end of the movie when Adrian is climbing into the ring, Rocky turns to her and for a very short time you can see the line between the make-up appliance used on his right eye to make him look beat up and the skin of his right cheekbone as well.
Continuity mistake: When a particularly unfit Rocky runs up the steps at dawn, it obviously takes a long time, as when he reaches the top and we go to a different shot, it's a lot lighter. When returning to the previous angle, it gets that little bit darker again.
Other mistake: About half way through the movie, Adrian gives Rocky a dog (Butkus). The second time Rocky goes to the the meatpacking plant, the dog is with him when he walks in, but he walks out alone and the dog is not seen again in this movie.
Continuity mistake: In the scene where Adrian is waiting for Rocky as he is returning home, she is going to surprise him with a gift, Butkus the dog. Rocky is standing about 25 feet from her so he has a good angle to see the entire porch. When she presents him with the dog, he acts surprised like he didn't see him on the side of the cement porch. Plus she is holding the dog leash in her hand. Rocky would have seen the dog immediately.
Continuity mistake: When Rocky goes to see Pauly at the meat market, Pauly places a steak in a wrapper and puts a small piece of tape on it. When Rocky leaves after hitting the hanging meat you can see that the piece of tape on the wrapper is much larger than before.
Continuity mistake: There is a dartboard in Rocky's apartment. During a touching scene between Adrian and Rocky, you can see the darts on that board change position between scenes. No one is playing darts at the time.
Factual error: When Rocky wakes up on the day of his first jog, the radio announcer reports that it's 28 degrees outside. However, when we see Rocky jogging, you can't see his breath.
Continuity mistake: In the last fight scene, particularly during the close-ups of the fighters, you can clearly see in numerous shots that the auditorium seats are empty. This is contrasted with the earlier shots where it is jam packed as the fighters are entering the ring.
Visible crew/equipment: When Rocky is talking to Mike in the locker room after his locker has been taken over by another boxer, when Rocky is talking you can see the shadow of the boom mic on the locker behind him as it dips in and out of view. As he starts walking away, you can also see it as it follows him.