The Japanese version didn't have a Story Mode save feature. For this reason, the option to erase Story Mode's save data is absent in Japanese version.
Contributed by Mr. Kite
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The game was originally called Yoshi's Island 64, and featured a logo strongly resembling that of Super Mario World 2: Yoshi's Island for the SNES, suggesting that Yoshi's Story was originally going to be a sequel.
Contributed by CuriousUserX90
Hitting the Spiders with an egg in the uppermost hut of the Jungle Hut level affects the instruments used in the music that plays during the level.
Contributed by CuriousUserX90
The newspapers in the background of the Jelly Pipe level say a variety of things, such as Luigi, Mario, Zelda, N64, Pikachu, Nintendo, Yoshi, and Nintendo 64.
Contributed by CuriousUserX90
There's an unused piece of music that sounds similar to the tracks for when a page opens in story mode.
Contributed by CuriousUserX90
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In prerelease footage of the game, a purple and brown Yoshi can be seen. They even appear in the intro. But for some reason, they were taken out of the game.
Contributed by Bean101