It left me questioning to myself how I would treat a loved one if I knew they were going to die. Would I treasure that relationship more? Would I be nicer, more patient, etc.? If so, then why am I not acting that way now? We're all going to die at some point. When and where and how shouldn't affect how we treat somebody. That point was made quite powerfully to me in the movie.
Also, the fact that she chose to have her baby knowing that she would die young and would have no power to stop it. Why? Because the joy and satisfaction of parenthood is worth the pain.
Aside from the details of the plot and circular time, those are the things that stuck out to me when I watched it.