In the Japanese version, the title screen for the Boss Butch minigame adds in a "Nintendo 16" logo parodying that of the Nintendo 64, which had been out for almost two years by the time the game came out in Japan. The logo riffs on the Super Famicom's nature as a 16-bit console.
The game's "Boss Butch" mode has a hidden screen that can only be seen if the player completes the mode without taking any damage and holds down the X, L, and R buttons just before the fade to black. The ending cutscene and credits will be replaced with an illustration of Kirby standing atop the defeated bosses with "PERFECT!" written above.
A spider-like enemy called Mariel is likely a reference to one of the angels from Neon Genesis Evangelion named Matarael, which is depicted as a spider-like being.
When going to the title screen, the logo in the Japanese version is animated while in the North American version it's not animated.
In the original release of the game, the background clouds in the Boss Butch battle against Dark Matter/Zero are blue and red. However, in the Virtual Console re-release, they are orange and green. This was most likely done to avoid any epilepsy effects.
The sixth and final level is called "Hyper Zone", which is a reference to one of HAL's earlier games of the same name. There are also levels named "Ripple Field" and "Grass Land", which were level names in Hyper Zone.
In stage 4-1 is a flower named Hibanamodoki. Hibanamodoki bears a strong resemblance to a fire flower from the Super Mario Bros series.
Metroids appear the second level of Iceberg. They can only be beaten with the ice power (mirroring how Samus needs to use the Ice Beam/Missiles to defeat them). When you beat the level, Samus is standing in front of the exit. If you beat all the Metroids, Samus will have her helmet off. This a likely reference to the typical Metroid convention of allowing players to get a glimpse of Samus's face by getting a 100% collection rating.