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.
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 is inside the pet store for the first time he picks up a can of turtle food and then reaches into his pocket. The next shot is side on and he is holding the can with both hands and Adrian, who was facing side on to the cash register, is now facing it.