Mario Part 5 - Did You Know Gaming? Feat. MatPat from Game Theory
There is unused ending dialogue between Luigi, Bowser, Mario, Yoshi, and a penguin.
Contributed by MeleeWaluigi
While the Koopalings guard each floor of Bowser's castle, two of them, Lemmy and Morton, don't appear in the game. However, a couple voice clips featuring each of them can be found in the PC CD-ROM release's files, suggesting that they may have been considered, either for the original release, or as additional content in the expanded CD-ROM version.
Contributed by KnowledgeBase
The game contains a reference to the Teenage Mutant Ninja Turtles. In the level "Rome", Luigi may be asked "Let's Make this picture perfect. Who painted the ceiling?" The possible answers are:
3 of those names are the members of the Teenage Mutant Ninja Turtles, whilst Splinter was their teacher and Sensei.
Contributed by CosmykTheDolfyn
In the SNES version, the debug menu can be accessed by pressing L, R, Select and Start on the second controller at the main menu.
Contributed by Antwan
In the disc-based version of the game there is an audio excerpt from the Star Trek: The Original Series episode "The Ultimate Computer". The quote is:

"Seminars and lectures to rows of fools who couldn't begin to understand my systems. Colleagues. Colleagues laughing behind my back at the boy wonder and becoming famous building on my work. Building on my work."

The filename, "PAT.WAV", may be in reference to one of the programmers, Pat McCarthy.
Contributed by DeerBoarDude