In the Japanese version, a small description/name will be displayed once you select a Robot Master.
In the English version, the player is always greeted by Dr. Light when they get a new weapon, who gives them information about it. But in the Japanese version they also meet Roll and Auto.
In the Japanese version of the game after Mega Man beats Dr. Wily and Spoiler:Wily says that robots cannot harm humans, Mega Man answers with "....." (which suggests that Mega Man is programmed with Asimov's Rules of Robotics). In the American version of the game, Mega Man says "I am more than a robot!! Die Wily!!" implying that Mega Man fully intended to kill Dr. Wily and break the Laws.
The password provided after completing the game provides access to a hidden feature in addition to its normal function. Confirming the password entry with the L+R+Start button combination will load a secret two-player versus mode, with Mega Man and Bass as playable characters.
In Shade Man's stage, right before you fight him, you will encounter Bass. In the SNES version he says "Damn!", while in the Anniversary Collection, it was changed to "Darn!". This was most likely done to avoid a Teen rating for the game (as the E10+ rating had not been made at the time of the original release).
If you use the Rush Search in a spot that does not have anything in it, there is a chance that Rush will dig up a Game Boy.
The theme from Ghosts 'n Goblins will play during Shade Man's stage if B is held while selecting the level.
During the intro sequence, Dr. Wily is mostly covered by other graphics. Extracting his sprite from the game will show that he has distinct breasts. The orientation of his shoulders and arms means they couldn't be pectoral muscles. This could simple be poor rendering by the artist but given the precise nature of pixel art, it is more likely be intentional or possibly a joke by the developers.