For the scene where Casper drags Kat out the window, and then takes her to the lighthouse, Christina Ricci had a piece of fishing line tied to her wrist, to give the appearance of being pulled by a ghost.
A musical scene, titled "Lucky Enough to Be A Ghost," was scripted and filmed. The three ghosts sang about their mental problems during a session with Dr. Harvey. It was dropped because of cost; the animation would have cost a few million dollars.
A live-action sequel was proposed, and a preliminary script was drafted, when production wrapped. Unfortunately, Christina Ricci and Bill Pullman were attached to other projects, and would not be available for more than a year. The producers decided to produce a cartoon series instead.
It's implicit in the doctor Harvey's possession scene by the three ghost uncles that the three cameos ( Clint Eastwood, Rodney Dangerfield and Mel Gibson) matches to each of the Casper uncles when they were alive (Stretch- Eastwood, Fatso- Dangerfield and Stinky- Gibson).
Clint Eastwood and Mel Gibson, the famous Hollywood actors, into whom Dr. Harvey changes, when he is possessed by Stretch, Stinky, and Fatso, are famous for playing vigilante policemen in classic action film franchises: Clint Eastwood is famous for playing Detective Harry Callahan in Dirty Harry (1971) and it's sequels, which Eastwood played from 1971-1988, and Mel Gibson is famous for playing Max Rockatansky in Mad Max (1979) and it's sequels, which he played for 1979-1985.