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While watching Casper, I couldn't understand why all the other ghosts (Kat's father and Kerrigan) look like ghostly, cartoonish versions of their living selves, while Casper looks just like the character in the old animated cartoons (complete with four fingers, which he lampshades), but looks nothing like himself when he was alive (his uncles would probably also count since their living selves are never shown). However, by the movie's viewpoint, it all makes sense since according to the film, ghosts slowly lose their memories of their former selves after death. That means as Casper's memories as a living boy eventually faded away, his original face and features also faded away until he looked like a generic ghost.
This doesn't quite work out, since Dr. Harvey appears to have lost all his memories (except for a general recollection of the partying) immediately after his death. It's also implied that Casper lost his own memories shortly after dying, or else he would have offered solid proof that his father wasn't crazy for thinking he was still around. Kerrigan probably only kept her memories for those few minutes after she died because she was so strong-willed, and because they related to her unfinished business. (She wasn't shown thinking of anything not directly related to the treasure or the Lazarus machine.)
Keep in mind that Kerrigan is the only one who died in a non-altered state of mind. Dr. Harvey was drunk when he died, and was acting uninhibited when his ghost appeared. Casper died of pneumonia, one of the symptoms of which is a high fever, which can affect your mental state especially in a time before 95% of modern medicines were discovered and the only thing you could do for a fever was pray it went away.
A smaller example. The movie takes place in Maine. Upon reaching the house, Kat mentions that it's a nice place if you're Stephen King. Stephen King grew up in Maine, and it is also where most of his stories take place.
When Dr. Harvey becomes a ghost, he presumably leaves his mortal shell behind in the open construction trench where he died. After entering the Lazarus machine, he gets a fresh new body ...so what happened to his old one?
It sounds like he took a nasty fall, so probably his old body is completely damaged.
I think the original poster was implying that a construction crew is gonna find his old body.