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.
Many of the actors pointed out to themselves a plot hole earlier in the filming of the movie: they wondered how the ship got out of Crystal Lake and into the Atlantic Ocean. Since most of them were just happy to be in a film they didn't bring it up to the producers or director. Actor Vincent Craig Dupree was quoted in an interview about the plot hole saying "this damn boat could have come from the Sahara Desert and gotten into the Atlantic". "I don't care, I'm not gonna challenge the concept".