The original Luigi's Mansion was developed with the Gamecubes stereoscopic 3D rendering ability in mind, which was ultimatively never used due the cost of the hardware needed to actually bring the effect out of a TV. Being able to have 3D effects was the reason why the sequel was developed for the 3DS rather than a home console.
The Sneakers are based on a scrapped ghost from the original, whose purpose was to give Luigi a health-crippling Jump Scare.
Market-Based Title: The game is known as Luigi's Mansion: Dark Moon in North America and simply Luigi's Mansion 2 elsewhere. This was done to raise awareness to the fact there was indeed another Luigi's Mansion game.
Short Run in Peru: The game was supposed to be released on March 29th, 2013, but wasn't, due to its launch coinciding with Good Friday, a Christian Holiday in parts of Europe. In response, Nintendo gave special permission to affected countries to release the game either a Day Early (Thursday), or a Day Late (Saturday). Some countries were very unfortunate to not get the game until the following Tuesday (as Monday was Easter Monday).
Milestone Celebration: Part of Nintendo's Year of Luigi, the 30th anniversary of Luigi's debut in Mario Bros.. Incidentally, the inclusion of Luigi's Mansion just happened to be by chance, since it wasn't developed for the anniversary in mind.