Revealing mistake: 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. (01:07:45 - 01:09:00)
Revealing 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... (01:49:20)
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.
Revealing mistake: During the fight, it appears that the filming is done in FF to make it more dramatic. If you look at the movement of the crowd, it seems to be sped up. Still, masterfully done on a low budget.
Revealing mistake: While Rocky is running through the small market, on the street people are looking at the camera.
Revealing mistake: When the first fight is about to begin, there are several shots of a crowded arena and people watching. The grainy and slightly blurry look of the film reveals they're stock images. The filming set had no budget to fill the place with people.
Revealing mistake: When the movie begins with Rocky and Spider fighting, their punches miss each other by far, though each one reacts as if they were hit. It is so obvious that it's ridiculous.
Suggested correction: As pointed out several times before, breath showing in the air is about humidity, not temperature. See Alien vs Predator for similar corrections.
This is a misunderstanding about how humidity plays a role in seeing your breath. If the relative humidity of both your breath and air outside combined is 100%, you'll see your breath, this means you can see your breath at higher temperatures. To reach 100% relative humidity, the outside humidity needs to be higher or the temperature needs to be lower. However, at a certain temperature (usually around 45°F), you'll always see your breath. So at 28°, you'll always see your breath, no matter what the humidity is. This is a valid revealing mistake.
Bishop73