If you take the first letter of the names of the 5 mansions as they appear in order (Gloomy Manor, Haunted Towers, Old Clockworks, Secret Mine, Treacherous Mansion), the letters appropriately spell "ghost".
At the end of the first Luigi's Mansion, you were given a new mansion, the size of which varied based on how much money you collected. At the beginning of the game, Luigi can be seen relaxing in a house that is very similar to the Rank D house (rewarded if the player collected 50,000,001 to 60,000,000 in gold).
During the opening cut-scene, the map that Luigi originally used in "Luigi's Mansion" is seen hung on the wall.
In the first boss mission, when Luigi enters the elevator, it is playing the pause music from Mario Strikers Charged. Both it and this game were developed by Next Level Games.
Of the three Luigi's Mansion games, Dark Moon takes the longest time to complete 100 percent, with 9 hours and 40 minutes.