Kane Hodder says that one of the most fun parts of his tenure as Jason were the scenes in Times Square. He says that spectators were lined up and down the block watching the filming and he didn't want to take off the mask to destroy their illusion of Jason. He said that every once in awhile he'd turn his head and look at them and watch them all go crazy.
According to an interview in Fangoria Magazine (August 1989), Kane Hodder vomited on cue in the final scene after drinking several pitchers of water. This was not a special effect.
Rob Hedden originally wrote more of the movie to be set in New York. He had written scenes at Madison Square Garden, the Brooklyn Bridge, the Statue of Liberty, and the Empire State Building. But despite the fact that this film had the highest budget of a Friday the 13th movie at the time ($5 million), Paramount told him that there wasn't enough money to film so many scenes in New York, so he was forced to rewrite the film and spend more time on the cruise ship; even most of the scenes set in New York were filmed in Vancouver. Hedden says he agrees with fans who complain that not enough time in the movie is spent in New York, given the title.
(at around 1h 28 mins) In the diner the man Jason throws into the mirror is Ken Kirzinger who would go on to play Jason in Freddy contre Jason (2003). Kirzinger also doubles as Jason in a few brief shots in this film.
Despite the nature of the film and adverse filming conditions, Kane Hodder provided several moments of levity which were appreciated by the cast. Following several death scenes, for example, once director Rob Hedden called "cut," Hodder would do a brief disco dance in full Jason costume and make-up making the cast laugh.