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 had 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.