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Mario Part 3 - Did You Know Gaming? Feat. Yungtown
 
The music that plays in the mini-game "Bobsled Run" seems to be based on the Giant Land Theme from Super Mario Bros. 3
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Mario Party supports the 64DD as a possible game add-on. While the US version displays a black screen when there's a 64DD attached to the system, the Japanese and European versions actually recognize the 64DD and check for a disk. If it's the wrong disk, an error will appear in either Japanese, English, French, or German depending on the selected language.
Contributed by GamerBen144
There is a track in the Japanese version not present in the NTSC release of the game called "Move to the Mambo". It plays during the mini-games Balloon Burst and Musical Mushrooms.
Contributed by CuriousUserX90
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Through the use of a Gameshark code, it's possible to enable a feature that ultimately went unused in the final game. After a player's turn ends, their HUD will turn yellow, and a big "NO GAME" sign will appear before moving on to the next turn, instead of playing a mini-game. If it's the last turn, a big "GAME OVER" sign will appear, and the board ending will play as normal.
Contributed by Bean101
Some of the game's voice clips are copied from the Japanese version of Mario Kart 64. This is true for all versions of the game.
Contributed by Boyobmas
The music that plays in the Mini-game 'Pedal Power' is a remixed version of the "Ice Land" theme from Super Mario Bros. 3.
Contributed by Worthiestnobody
In the Japanese version of the game, both Wario and Luigi had different "MISS" lines. If they failed or "Missed" (like got to Bowser or lost a mini-game), they would say "Oh, my god." They changed it so Wario would say "Doh, I missed" and Luigi to say, "Ohhh" instead.
Contributed by gamemaster1991
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There are a few mini-games which were cut but can still be found in the game's files. The games are All or Nothing, Tour de Mario, Bungee Jump, Same Game, and Yoshi's Tongue Meeting. Some of them are playable and can be accessed with the use of a GameShark device.
Contributed by KnowledgeBase
Nintendo used to provide padded sports gloves for gamers who called in and asked for them. This was because some of the mini-games forced you to use your palm to rotate the control stick. This led to injuries include blistering, burns, lacerations, punctures, and cuts. The damages resulted in a law suit which led to Nintendo potentially giving out $80 million of padded gloves.
Contributed by gamemaster1991