I just watched The Girl Who Leapt Through Time and it was very good but I have several outstanding questions, which so far the Internet has not helped me with:
How does the girl remember the timeline (in which her two friends die on a bike) that her friend changed?
How does her friend stop time?
Where did her friend disappear to, after he had used up all his time leaps? Does he just disappear into the crowd and walk away?
If leaping through time only moves your consciousness, not your physical body (as evidenced by no duplicates), how does he travel back to (presumably) a time period before he was born? Or, if leaping through time does move your body (as evidenced by the crashing into things upon arrival), why are there no duplicates of him, or her?
How does her aunt know so much about time travel? Best answer: she is the girl, grown up, traveled back from the future to save the painting.
Why is the painting so important?
What cataclysm happens in the future to make a world with no baseball and no sky? More importantly, if everyone has time travel, why don't they prevent it?
Ok, and now we finally saw Somewhere in Time, starring Christopher Reeve and a beautiful Jane Seymor. Not bad, for what it was, which is an unabashedly cheesy romantic film. Have you seen it? A few lingering questions - which I kind of like that it doesn't answer:
I really expected the manager to be a time traveler, too. I guess I've seen too many science fiction movies, and this stuck to a simpler romance. But what if he was? They never explained how he knew to expect Richard.
Did the woman figure out that Richard was a time traveler and look for him for 60 years? Or did she happen to stumble upon his first play, and then realize it when she saw him? That must have been surprising.
As Rachel pointed out, it would have made more sense if, instead of later dropping his revelatory 1979 penny in 1979, he dropped it in 1912 ... and that was how she realized he was a time traveler and knew to wait til the 1970s.