I have the basic Moogle Throw ability - but where do I get the "improved" version which allows me to access certain items I can't otherwise reach?
At some point in Episode 3, you'll unlock Serendipity -??? AF-, which is like a giant casino. There, you'll meet a mystic who will teach you about skill fragments.
She'll also give you Mog's Manifestation as part of a starter package of skill fragments: this fragment provides Improved Moogle Throw.