Continuity mistake: When Apollo Creed is approaching the ring for the rematch at the end of the film, his robe starts off done-up, next shot shows it undone and the towel around his neck loose, and then in the last shot it's back to being neat again with the robe done up. Even when he enters the ring it's all neat and tidy.
Continuity mistake: In the scene where Rocky is proposing to Adrian at the zoo, there are clumps of snow on his right shoulder. When he leans in towards Adrian to pull back her earmuff, the snow is gone. When he goes to kiss her, the snow reappears. When they walk out arm in arm, the snow disappears again.