This entire episode is a parody of the plot, characters, scenes, dialogue, and even shots, of the movie Titanic. The title, however, is a reference to Walter Lord's "A Night to Remember," a book/movie detailing the last hours of the doomed liner.
The bartender robot, iZac, is a parody of "Isaac", the bartender on the show, The Love Boat and of the "iBook" and similar Products by Apple.
The use of the Titanic as a luxury spaceship is a reference to Douglas Adams' book "The Hitchhiker's Guide to the Galaxy" in which a similarly named starship suffers "a spontaneous massive existence failure." There is also a video game entitled "Starship Titanic" produced by Adams.
In an attempt to cheer Bender up, Fry mentions that the Countess could still be alive in another dimension, to which the Professor secretly confides in Zoidberg that there's "not a chance" and implies there's no doubt she's dead, which debunks the theory of entangled black holes forming a wormhole and also the relative uncertainty on what actually happen in a black hole.