Well, isn't that strange. This is what I've got from my reference which is Thorf's Final Mix Changes FAQ from GameFAQs...
Final Mix -------------------------------------------------- ファイナルミックス
-------------------------------------------------------------------------------
Original Secret Movie
- Finish the story on all worlds
- Rescue all of the 101 Dalmatians
Final Mix Secret Movie
- Fulfil the conditions for the Original Secret Movie
- Complete the Jiminy Memo section so that a yellow Mickey icon appears
Finishing the story on all the worlds presumably entails following the story to the end on each world, i.e. locking all the keyholes and finishing the Jiminy Memo Story So Far section, so that you get the yellow Mickey icon for it.
Completing the Jiminy Memo section means completing and getting a Mickey mark next to all the sections, at which point one will appear next to the Jiminy Memo button on the main menu. See the Jiminy Memo section of this FAQ for details.
Final Mix: Proud --------------------------------- ファイナルミックス:プラウド
-------------------------------------------------------------------------------
Original Secret Movie
- Just finish the game; no special conditions
Final Mix Secret Movie
- Finish the story on all worlds
- Win the normal round of the Hades Cup
As you can see, it is infinitely easier to get Deep Dive to display on Proud level.
Now I'm confused. I remember having missed a few entries in the Journal, yet I was still able to watch Deep Dive...