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Mario Part 4 - Did You Know Gaming? Feat. Yungtown
 
In the "Big Donut" battle stage, there are 2 hidden item boxes that can be seen under the track. They're inaccessible, and were likely just left over from development.
Contributed by DarkJedi
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The idea for the Blue Shell came to mind after processing limitations prevented the developers from showing all of the characters on screen at the same time. Their solution was to clear an overcrowded track with using the Blue Shell.
Contributed by CuriousUserX90
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The trophy ceremony in the Japanese version displays the text "You are in (position)". The American version changes this to "You placed (position)". The punctuation was also removed.
Contributed by FalseFruit
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The Japanese version The course "Moo Moo Farm" is called "Moh Moh Farm". This is because the Japanese onomatopoeia for mooing sounds like "mō mō", with a long "O" sound.
Contributed by FalseFruit
To date, the only course from the game that has not appeared as a retro course in later Mario Kart games is "Wario Stadium".
Contributed by CosmykTheDolfyn
In the Wii Virtual Console version, the lightning power-up's visuals were changed to reduce the intensity of the flash. This was likely done to avoid causing seizures.
Contributed by Boyobmas
The Game originally had a Vertical Split-screen in 2 Player gameplay. This cannot be done without hacking in the Final Version, and the Lap Counter still appears in Battle Mode. Mario Kart 8 later managed to use Vertical Split-screen 18 years later.
Contributed by CuriousUserX90
Thwomp's laugh is actually Wario's laugh slowed down. Since Wario's original voice from the Japanese release was changed in the Western version to sound more fitting, Thwomp's voice was also affected.
Contributed by CuriousUserX90
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Twice as many people are credited as voice actors in the Japanese version compared to the American version, with Charles Martinet being the only one to provide voices for both versions of the game.
Contributed by game4brains
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Charles Martinet's name is misspelled "Charles Martinee" in the credits of the Japanese version.
Contributed by game4brains
Luigi, Peach, Toad and Wario's voices were changed in the Western releases of the game from those used in the original Japanese version, despite already being in English. It's thought that Nintendo of America felt the original voice clips did not properly represent the characters, or were simply of poor quality. However, the original Japanese voices were later used in the first two Mario Party games in the worldwide releases, as well as Mario Kart: Super Circuit.
Contributed by CuriousUserX90
The voice clips for each of the menu options in the Japanese version of the game are in English, but the speaker has an inconsistent accent, and emphasizes each word in an unnatural manner. These voiceovers were replaced with Mario's voice in the international releases.
Contributed by xianc78
If the player places 4th or 5th overall in a Grand Prix, they will be shown a cutscene where their character looks on at the winners, sadly drives off, and then gets blown-up by a Bob-Omb. The game then shows a message that says "What a Pity! You placed 4th/5th; Maybe next time!" Throughout the cutscene, the music changes from the standard fanfare to a more bleak version when the losing character drives off, and soon slows to a stop when the Bob-Omb appears.

If the player places in the top three, it's also possible to see the 4th place character in the distance for a brief moment, alluding to the hidden cutscene.
Contributed by game4brains
Letting the music on the results screen loop 64 times (roughly 50 minutes) causes the music to change, playing an alternate hidden version of the "results" theme.
Contributed by DidYouKnowGaming
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In its early beta stage, the game was known as Super Mario Kart R. Some differences were Kamek as a playable character who would later be replaced with Donkey Kong. Also there was an option to have the multiplayer screen set to horizontally or vertically, but this was removed in the final version. A number of other small differences were the avatars in the "Character Select" screen, the textures of the "Item Boxes", the feather as an item, and other minor graphic details.
Contributed by KnowledgeBase
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Originally, there were several nods to real world products such as Marlboro Cigarettes, Agip Gasoline, Mobil1 Oil, Goodyear, and 76 Gas Station. They were altered internationally for two likely reasons; One of the companies parodied sold cigarettes (possible trouble for an E rated game) and any of them could have sued.
Contributed by Berry