The music used in the game's opening cutscene, main menu/map screen, and end credits is taken almost note-for-note from Max Steiner's "Polka Melody", featured in the 1933 film adaptation of the novel "Little Women".
Contributed by MehDeletingLater
As Mario and Luigi approach Ludwig's hotel, Mario comments "We ain't afraid'a no Koopas!", a reference to the theme song to the 1984 film "Ghostbusters".
Contributed by MehDeletingLater
After Mario, Luigi and the Princess run out of Lemmy's hotel, a giant fan is switched on blowing Lemmy and the hotel away, to which Mario says "Hey you! Get off of my cloud!". This is a reference to The Rolling Stones' 1965 song "Get Off of My Cloud".
Contributed by MehDeletingLater
When Mario jumps on an enemy, the hit effect sprite that briefly appears features a vague picture of a Peace sign.
Contributed by MehDeletingLater
Bowser and the Koopaling's hotels are all references to real-life and fictional hotels:
•Morton's WoodDoor-Hysteria = Waldorf Astoria
•Roy's HardBrick Hotel = "Heartbreak Hotel" by Elvis Presley
•Larry's Chillton Hotel = Hilton
•Lemmy's High-ate Regency Hotel = Hyatt Regency
•Ludwig's Thump Castle Hotel = Trump's Castle
•Wendy's Blitz Snarlton Hotel = Ritz-Carlton
•Bowser's Seizures Palace Hotel = Caesars Palace
Contributed by MehDeletingLater
In the English version of the game, Bowser's laugh in the opening has a noticeable echo to it. This is oddly absent from the French release of the game.
Contributed by billebobfacts
There is an unused help dialog that uses the same voice for Mario as the unused cutscene for when the player defeats Roy.
Contributed by xianc78
An early version of the cutscene that plays when you beat Roy doesn't use the voice actors from the final game. The voices of the Mario brothers seem to be heavily based on Walker Boone and Tony Rosato's takes on the brothers from the Mario cartoon series airing at around the same time. Oddly enough, this is stored in the data for the final level, not Roy's. There is no known cutscene data.
Contributed by billebobfacts
Iggy Koopa is the only koopa without a hotel. However, looking through the game's data reveals each hotel has an internal music, graphics and enemy data file labeled from L1 to L8. L6 is missing in its entirety, and the game jumps from Ludwig's to Wendy's hotel (L5 to L7).

You can extract sound and cutscene data from L6, but the hotel is left entirely blank. This points toward Iggy being planned to have a hotel of his own, opposed to only appearing in Bowser's hotel.
Contributed by Outofmind23
Depending on the day the CD-i's clock is set to, very brief messages will appear underneath the loading screen of the game's first level in place of the standard "HERE WE GO!" message:

•January 1st = "HAPPY NEW YEAR!"
•February 14th = "HAPPY VALENTINES DAY!"
February 17th = "ITS HOLLIES BIRTHDAY!", celebrating the birthday of Play Consultant Hollie S. Lohff.
•August 31st = "READY TO GO BACK TO SCHOOL?"
•October 31st = "BOOOOOOOOO!!!"
•December 25th = "HAPPY HOLIDAYS!"
•December 31st = "HAPPY NEW YEAR!"

In regards to the February 17th message, Hollie S. Lohff is the daughter of one of the game's engineers, Thomas Lohff. She was brought in to playtest the game and commented that Mario should be able to jump, as it was weird to play a Mario game without that mechanic. The developers took her advice and added her to the game credits as "Play Consultant."

The French version of the game features its own unique messages to indicate French holidays:

•January 1st = "BONNE ANNEE" ("Happy New Year.")
•Late January = "ALLONS CHERCHER LA FEVE" ("Let's find the charm." Displays in a time of year where in France the people eat some "Galette des Rois" (King's Pie) and there is a charm hidden in the pie.)
•February 14th = "C'EST LA SAINT VALENTIN" ("It's Valentine's Day.")
•Carnival celebration in France = "ON SE DEGUISERA POUR LE MARDI GRAS" ("We'll be dressing up for Mardi Gras.")
•Easter = "OU SONT CACHES LES OEUFS" ("Where are the eggs hidden?")
•Last Sunday in May = "BONNE FETE MAMAN" ("Happy Mother's Day, Mom!")
•May 31st = "L'ECOLE EST BIENTOT FINIE" ("School is almost over." Displays when most schools began Summer vacation at the time.)
•Third Sunday of June = "BONNE FETE PAPA" ("Happy Father's Day, Dad!")
•July 14th = "ALLONS ENFANT DE LA PATRIIIIEEE" ("Arise, children of the Fatherland." Displays on France's national celebration. Taken from the French national anthem "La Marseillaise", although "ENFANT" should be "ENFANTS" due to the plural grammar rule.)
•August 31st = "PREPAREZ VOS CARTABLES" ("Prepare your schoolbags." Referring to returning to school. Displays when most schools were ending Summer vacation at the time.)
•December 25th = "JOYEUX NOEL" ("Merry Christmas.")
•December 31st = "BONNE ANNEE" ("Happy New Year")
Contributed by pyoro64