In Paper Mario: Sticker Star, if Mario picks up a HP-Up Heart while dying, he will be trapped in a purgatory-like black void where he is stuck constantly repeating his death animation, but unable to actually die.
In Paper Mario, Parakarry is a clumsy postman who joins Mario to find letters he lost. However, at the end of the game, Parakarry leaves, while the letters never actually get removed from Mario's inventory. This creates the humorous effect of Parakarry forgetting them once again.
In Super Paper Mario, Bowser can accidentally break the game at the worst possible time purely due to how large he is. His size allows him to open two chests at once at the bottom of the Pit of 100 Trials, which will freeze the game and undo vast amounts of progress.