The song that Malachi played throughout the episode was "When the Saints Go Marching In".
Peter is more concerned with going to Mardi Gras but the other Ghostbusters aren't able to tell him it's over already by the end of the episode. This places the episode ending about the day before Ash Wednesday in mid-February.
In keeping with Ghostbuster tradition, Ray is the only Ghostbuster to be possessed (Preternaturally induced hypnogogic ataraxia as Egon calls it). Ray's susceptibility to ghostly mental manipulation can be seen in both movies and several episodes of The Real Ghostbusters.
Marie admits to being a Mambo, a priestess of Voodoo. She uses ritual powder on Malachi.
Among Egon's many techno babble lines he remarks that Malichi may cause a "chrono-synclastic infundibulum." This is a term used in "The Sirens of Titan" by Kurt Vonnegut to describe a wormhole-like phenomenon.