Other mistake: About half way through the movie, Adrian gives Rocky a dog (Butkus). The second time Rocky goes to 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.
Suggested correction: How is this a mistake? Rocky could easily have left with the dog on another occasion. It's like saying, sometimes Rocky is shown in a location but it's never shown how he got there. That isn't a mistake, it's just what happens in films. Also, the dog not being seen again is irrelevant.
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)
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.