Another moment that gets to me is during the night when Littlefoot wakes up and sees the frog and chases after it, when you know what it leads to. And how he inadvertently caused his own mother's death that way. Even the soothing yet somber music that plays right as he wakes up (4:48 on the "Sharptooth and the Earthquake" track). The movie just has such a haunting quality to it.
One other thing I noticed is that, right after Littlefoot and Cera's fight, it plays a reprise of the theme where Littlefoot's mother dies. As if this movie couldn't get any more sad.