I watched this movie when I was in rehab. It has become my favorite movie. It's symbolic of:
Romans 8:28 KJV — And we know that all things work together for good to them that love God, to them who are the called according to his purpose.
Even when we sin, God still uses it for good. The key point isn't how she forgave his transgression, but how she changed for the better. But notice how he only changed after she left him. "absence makes the heart grow fonder".
Proverbs 22:6 KJV — Train up a child in the way he should go: and when he is old, he will not depart from it.
I found it fascinating that even God showed up (the captin), and it wasn't until Jim made a commitment to providence that Aurora accepted his authority.