The Common Hatred

In Super Mario World, Mario's punching animation when he is climbing on the backside of a fence suffers from a discoloration in his arm, whereby part of it is pink.

Top: this can be seen most easily as Fire Mario, since the pinkness of the arm does not change even when Mario's shirt changes colors to white. The footage uses a glitch whereby a well-timed jump off a rotating panel can cause Mario to climb while mostly unobscured, showing the pink arm more clearly.

Bottom: this is an oversight resulting from how the game stores sprites. Each sprite is made out of 8x8 pixel squares (which are called "sprites" on the hardware level, not to be confused with the colloquial term "sprite" meaning the full image of a character) whereby each is assigned a palette. The two squares on the right, containing Mario's arm, are accidentally assigned a different palette (also visible by the outlines becoming black instead of remaining brown).

Source: MrPyt1001, Kaizoman, Mister Man

In Mario & Luigi: Brothership, in the build-up to Chilliam and Burnadette's wedding, Mario and Luigi are asked to get a wedding cake. The friendly NPCs all suggest getting a cake from Slippenglide Island while the Extension Corps make a plan to lure Mario and Luigi into a trap with a brochure about a cake from Lottacoins Island.

Since getting the Lottacoins Island cake requires trusting the Extension Corps, most players are more likely to decide to get the Slippenglide Island cake instead, and would not see both cakes unless doing two playthroughs of the game.

Above are the models for the two cakes (top: Slippenglide, bottom: Lottacoins) extracted from the game's files.

Source: DogToon64

Packaging of an officially licensed 1996 Super Mario 64 jigsaw puzzle from Japan.

A panel from a 2017 issue of the official Futurama comic series (Issue 83, "Bendocchio!") features a reference to the Mario series by including a couple consisting of a character who is almost identical to Mario except for a lack of an M emblem and an additional set of overall buttons, and a princess character who is very similar to Rosalina except recolored to Peach's color scheme.

In Paper Mario: The Thousand-Year Door, being Electrified is a purely beneficial status condition for anyone who receives it (whether it is Mario's party or an enemy), as all it does is deal contact damage to whoever attacks that character with a non-ranged attack.

However, it turns out that in the game's code, an unused functionality for Electrified exists that would have made it act more like the Paralysis status common in RPGs (e.g. like the Pokémon series games), whereby it would also have a chance of preventing the afflicted character from making a move on that turn. Note how in the footage, Mario and Goombella only briefly shake instead of being able to perform their attacks.

This actually explains an odd behavior in the game whereby enemies would sometimes use items to cure Electrified when it never needed to be cured in the first place (bottom image, dramatization from an earlier post explaining this phenomenon). These enemies must be acting upon a script written under the assumption that Electrified is still able to incure the Paralysis-like effect, which was not updated when the effect was removed during development.

The Spiky Goomba in the scenario means well, he is simply acting on outdated information.

Extremely rare officially licensed 1981 Donkey Kong arcade foil balloon, featuring a unique redrawn version of the cabinet side artwork with additional detail and shading.

In 2015, the official Rayman Twitter account posted three images featuring parodies of Mario-related Nintendo games featuring Rayman in Mario and Luigi outfits.

Top: a parody of the Donkey Kong arcade. Middle: a parody of Super Smash Bros. Bottom: a parody of Luigi's Mansion.