Other mistake: When Rocky is in the funhouse looking at himself, he appears to look relatively "normal". But it's very obvious that it's got nothing to do with the mirror, and more to do with the removal of a lot of makeup. For example, Rocky usually has almost no nose, but in the mirror he has Eric Stoltz's very well developed nose.
Other mistake: In the scene at the carnival, Rusty orders a lemonade at the concession stand and does not pay for it.
Continuity mistake: At the end of the movie a big man is placing flowers at Rocky's grave. From the back of the tombstone he is laying the flowers on their sides. In the next shot, from the front of the stone, they are standing up, leaning against the stone.