Found within the game's data is an unused Victory Dance Remix of when Kirby clears a level that's been used in various Kirby games over the years.
In level 3 of Neo Star, the word "KIRBY" can be found spelled out in rock formations towards the end of the level.
The tune that plays when Kirby collects an invincibility candy is different from the one played in every other Kirby game to date.

There was an early idea for a music based mini game in which players would play along to sheet music with Kirby, Ribbon, Adeleine, and King Dedede, but it was never implemented.

In the Japanese release, the sandwich was originally an onigiri. This was due to Nintendo regulations on Japanese culture when games were translated overseas. Oddly, Waddle Dee eats a onigiri during the stage ending picnic sequences in all versions.
The electric/cutter mix ability is most likely a reference to Darth Maul's dual sided lightsaber from the film Star Wars Episode I: The Phantom Menace.
Masahiro Sakurai (the creator of Kirby) provided the voice of King Dedede.
Shiver Star, the game's 5th world, appears to be a frozen-over version of Earth, containing several uninhabited urban areas. Nintendo has confirmed that Shiver Star was once inhabited, but the climate drove them to evacuate the planet. This has led fans to speculate that Shiver Star is a post-apocalyptic version of Earth. Though Nintendo's intentions during the making of Shiver Star remains unknown, it can be inferred that the world is either a message about climate change, or the suggestion that the "Kirby" series takes place in our own universe.