Cameos
Wii Fit
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There are multiple signs that parody Wii Fit, such as the Launch Fit, Slide Fit, and so on. The signs refer to them as "The Mushroom Kingdom's latest fad."
Dr. Mario Virus
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The enemy Toothy uses an attack where it spits out the Blue Virus from Dr. Mario.
Sockop
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Sockops are green, sock-like enemies based on the both the real-world pitcher plant as well as the Goomba Shoe (aka. Kuribo's Shoe) from Super Mario Bros. 3. When Luigi is later able to communicate with the Sockops, one reveals that its name is Kuribo.
Shroobs
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Fawful Theater
In the Fawful Theater, you can see dozens of Mario enemies in the seated audience. In the bottom-right corner of the room you can see a lone Shroob from Mario & Luigi: Partners in Time. It is also the only member of the audience you can interact with, although it only says "…"
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Bowser's Castle Cold Room
Later in the game you can fight an optional boss battle by entering the Cold Room in Bowser's Castle. The battle is against three Shroobs, and various other kinds of Shroob can be seen in the background.
References
Throughout the game, a number of references are made to Nintendo games or popular phrases:
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A Winner Is You
When Bowser is ejected from the Mushroom Kingdom at the start of the game, he is greeted by a mysterious tradesman with the phrase:
"A WINNER IS YOU!"
This is based on the poor English phrase first seen in Pro Wrestling on the NES.
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It's a Secret to Everybody
The Toad in Toad Town who teaches you about digging up beans uses the phrase "It's a secret to everybody".
This is a well-known phrase used by characters hidden in secret caves in The Legend of Zelda on the NES.
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Mouser
In the Fawful Theater, there is a brainwashed Goomba who is trying to remember who he used to work for, listing off words that rhyme with "Bowser".
One of the names he suggests is "Mouser", who was the first boss in Super Mario Bros. 2.