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 enhance her classic look.
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.
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 "first nation"
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.
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).
Wednesday and Pugsley's old-fashioned swimsuits are Victorian styles, circa the late 1800's to early 1900's (Victorian era). In fact, throughout the film, numerous references and styles from the Victorian era are seen in the Addams household. The modest black clothes, towering house and the decor are all from the Victorian and Edwardian era. The family has very few modern items or fixtures in the household (though we see Debbie watching TV).
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.
After the bachelor party Gomez is seen making a bottle for Pubert with strange ingredients such as Worcestershire Sauce and a raw egg. This is an old hangover remedy sometimes referred to as 'Hair of the Dog', although 'hair of the dog' can also refer to drinking the same beverage that got you drunk the night before. Gomez then gives the bottle to Pubert and says 'Hair of the Pup'. Pubert is wearing sunglasses, implying a hangover.
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.
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.
When Joel is showing Wednesday and Pugsley his "Serial Killers and Schizos" cards, the two in his hand besides The Black Widow are James Earl Ray and Lizzie Borden. Christina Ricci (Wednesday) would go on to play Lizzie Borden in a 2014 made-for-TV biopic, Lizzie Borden Took An Axe, and short-lived 2015 spin-off TV series, The Lizzie Borden Chronicles, both on Lifetime.
Debbie makes reference to the fact that Fester has an IRA. Assuming the movie is accurate, that means Uncle Fester had a job that paid him wages and he made deposits in an effort to obtain a tax break.
The license plates on Debbie's two cars (a Lincoln Town Car and a Mercedes-Benz SL) read "New York - A Nice State". They are a fictional design, the license plate slogan for New York is "The Empire State" (although this was absent from New York plates during the period this film was made) and the real design at the time consisted of blue lettering on a white background framed with two horizontal red stripes, with an image of the Statue of Liberty outlined in red. The plates in the film use green lettering on a white background surrounded by a green border (with no State of Liberty).
The trivia items below may give away important plot points.
Near the end of the film when Uncle Fester meets Dementia (his love interest), he says "Dementia what a beautiful name". This is very similar to what Doc Emmett Brown says in Back to the Future Part III (1990) when he meets Clara (his love interest) "Clara what a beautiful name". Christopher Lloyd played both roles.
20 years after this movie was released, it was revealed that Christina Ricci didn't like kissing David Krumholtz. During filming, she kept complaining that he had a peach fuzz on his upper lip. She didn't like that.