In 1990, Nintendo rebranded this game's title from Mike Tyson's Punch-Out!! (1987) to simply "Punch-Out!!" and re-released it in the United States after their license with Mike Tyson had expired. The removal of Tyson's name and likeness from the game was not related to Tyson's arrest, and later conviction, of rape, which occurred a year after Nintendo's rebranding.
One thing Doc says between matches is "Join the Nintendo Fun Club today, Mac!" The Fun Club was a subscription newsletter service the company offered beginning in January 1987. They offered advice, game strategies, and more. Nintendo replaced the Fun Club with Nintendo Power magazine in 1988.
King Hippo from this game was featured as a regular antagonist on Nintendo's cartoon series Captain N: The Game Master (1989). Unlike in this game, the animators made Hippo's skin blue.
When Mike Tyson appeared on Daniel Radcliffe/Mike Tyson/Sturgill Simpson (2014) on October 28th, 2014, host Jimmy Fallon challenged Tyson to defeat his virtual self in this game on live TV. The real Tyson was defeated in the first round and lost by TKO.
Nintendo had very stringent censorship morals in this period. Accordingly, the character called Vodka Drunkenski in the arcade version had his name changed to the (less offensive) Soda Popinski.