The "Scuba Steve" action figure in this movie is a fictional doll made up by Adam Sandler. "Scuba Steve" is based on a doll that Adam Sandler owned when he was a child, called Diver Dan. Diver Dan can be seen briefly in the intro scenes of another Dennis Dugan film, Problem Child (1990).
While filming, "The Waterboy" came out and was a huge success. Noticing the box office, Sony sent a memo to the set, letting the production team and Sandler know that they had extra money to film/expand scenes they felt were lacking. This allowed smaller characters played by Rob Schneider and Steve Buscemi to have greater roles.
Cole Sprouse and Dylan Sprouse both lost baby teeth during production and had to be fitted with temporary replacements. Dylan Sprouse's tooth fell out in the middle of a take. Near the end of the movie, just after entering Hooters for his birthday, Sonny makes a reference to Julian about dealing with a missing tooth (at around 1h 25 mins) while holding Julian, "Hey, You! Still missin' that tooth?").
Near the beginning of the movie when Sonny (Adam Sandler) is arguing with his girlfriend, she makes the comment that "the delivery guy is like your best friend." Rob Schneider, who plays the delivery guy, is in fact Adam Sandler's best friend in real life.
The young boy, Julian, was not actually one person, but two people; twins used for the movie. Famous from shows like Friends and The Suite Life Of Zac and Cody, Dylan and Cole Sprouse played the role of Julian.
Julian, Sonny and the delivery guy, while on the couch watching t.v., they were watching an episode of "Columbo" (1971), the director of this film, Dennis Dugan, played a detective on an episode ('76) of "Columbo".
When Frankenstein and Sonny come out of the store wearing white suits and white ties that was an obvious nod to "Twins" (1988). In Big Daddy there were not story similarities to Twins except for the size difference between Arnold Schwarzeneggar to Danny DeVito and Adam Sandler and Cole/Dylan Sprouse.