Adding more than just make up to the character, Morticia Addams is always lit separate from everyone else in a scene. Her lighting always consists of one beam of light across her eyes that gradually fades outward to add to her grim look.
Michael Jackson was signed on to write and perform a song for the film's soundtrack and to promote it with a video. Although he was able to finish the song, contractual difficulties coupled with the child molestation allegations made against Jackson resulted in the song being dropped from the soundtrack, and the video was never filmed. The song, "Is It Scary," was later included on Jackson's 1997 'Blood on the Dance Floor: HIStory in the Mix' album and was also used in his short film Ghosts (1997).
David Krumholtz's character says at one point he has every card for his Serial Killer Card Collections "except Jack the Ripper and that Zodiac Guy." Jack the Ripper and The Zodiac Killer are the real world's most famous uncaught serial killers.
The baby's name, Pubert, was the name originally suggested (and rejected) for Pugsley by Charles Addams when he was asked by the producers of The Addams Family (1964) to name the hitherto unnamed characters in his cartoons.
When Fester announces his engagement, Morticia makes an overt reference to the ring worn by Debbie being the same one in which Fester's grandmother was buried. Debbie slyly whips out a shovel, adding a literal component to her character's "golddigger" status.
Wednesday bitterly quips that "Chippewa" in Camp Chippewa means "orphan". This is pure sarcasm; Chippewa is actually a form of the name Ojibwa (a Native American nation), the original meaning of which is unknown.
Not only is Gary's play "puerile and under-dramatized" (as Wednesday puts it), it's historically inaccurate. The Chippewa are from the Midwest. Pocahontas was a Powhatan, a tribe indigenous to Virginia. Neither she nor the Chippewa would've been present at the first Thanksgiving. Moreover, by 1621 (the first Thanksgiving), Pocahontas had already married John Rolfe, moved to England, and died.
The mentioning of Debbie's axe-murder of her second husband (and Gramma's nostalgic sigh when she sees the slide) is a reference to the Addams family's having many ancestors/past cronies who were infamous serial killers, such as Zodiac, The Axeman, Jack the Ripper, Lizzie Bordon, etc. Wednesday and Pugsley's geeky summer-camp pal has a card collection of serial killers.