The family scene was nearly cut out of the final film due to lack of relevance with the film's plot. However, the Klump family turned out to be one of the most popular elements of the film, so much that the Klumps got a greatly expanded presence in the sequel, Nutty Professor II: The Klumps (2000).
When Eddie Murphy was interviewed by Jay Leno on The Tonight Show with Jay Leno (1992) in 1996, Jay asked if he would appear in public as one of these characters. He said he went outside walking down the street as Sherman Klump and was getting odd looks from those seeing him.
Reggie's "Birthday" joke about Sherman is technically incorrect. He compares Sherman's size to that of the Earth. Turning around in a circle would only amount to one day. He would actually have to orbit around a mass comparable to the sun to obtain a year passing. However the point of the joke was clearly easy to comprehend.
This movie has a lot in common with the Jim Carrey movie, The Mask (1994). They both have scenes that include transforming into the other self that is crazier than the normal self, romantic relationship with a woman, lying to cover up the other self, etc.
When Jason witnesses Buddy transform back into Sherman, Jason says "Oh, man! This is Freddy Kruger shit, man!" which is a nod to A Nightmare on Elm Street (1984) starring Robert Englund as the evil child killer Freddy Kruger who stalks his victims in their dreams after he was burned alive by a mob of angry parents.