Visible crew/equipment: Outside the chapel, when Frank backs into the pedestal the statue begins to topple over. In the shot facing up, as the pedestal falls and Frank puts his arms out to catch the statue, the wires used in this stunt are perfectly visible. (01:35:05)
Continuity mistake: When Mrs. Waterhouse walks into the livingroom and greets her three babies, there is a large area rug in front of the coffee table. However, as the babies fly towards her in the wide shot facing her, that area rug is gone! (00:22:55 - 00:23:50)
Revealing mistake: After Lucy discovers Mrs. Bradley in her bed, as she fights off and runs from Patricia, it is obvious that she wears knee pads for these shots.
Continuity mistake: At the cemetery, as Frank grabs Ray the ghost to pull him from his grave, the grave diggers are seen shoveling dirt into the half-filled hole. A few seconds later, Frank yanks Ray out and the grave is now completely filled and the grave diggers are gone.
Continuity mistake: When Frank returns home from the Lynskeys, he parks his Volvo right beside the outdoor fuse box post, with the box facing beyond the trunk of the car. However, after Frank goes upstairs, in the next exterior aerial shot the Volvo is 10-15 ft. away from the fuse box post and the box now faces beyond the front of the car. (00:17:30 - 00:19:20)
Revealing mistake: As the three babies fly towards Mrs. Waterhouse, when they land on her it is blatantly apparent that they're merely three dolls in this shot. She actually grips two from behind and the center doll is attached to her as she moves backwards. Also, in the shot facing the babies the center baby is in the bouncer seat with the rod attachment overhead, yet, in the shot facing Mrs. Waterhouse the rod attachment is gone. (00:23:50)
Continuity mistake: At the Bradley house, when Patricia runs to and then up the stairs, to try and get away from the ghost, the blood stains on Patricia's white robe change position. (00:02:10)
Continuity mistake: After Frank destroys Ray's fence, he backs the car over Budzo (the ceramic little gnome), crushing it on the lawn. Yet, when Ray picks him up crying out, "Oh, my Budzo! My Budzo!" he is holding the gnome's uncrushed head! (00:07:05)
Continuity mistake: At her house, Patricia runs away from the ghost and when she first enters the kitchen the countertops beside the sinks are completely bare. However, a few shots later there are neat stacks of china on the countertops, ready to fly off in the mayhem! (00:01:45)
Continuity mistake: Frank catches the statue, that he accidentally knocks over near the chapel. The way he catches it is completely different in the first shot facing up and the next close-up. (01:35:05)
Revealing mistake: At the Fairwater Tuberculosis Sanatorium, when Agent Dammers shoots Frank in his left arm, the white wrapping around his arm, where the bullet holes appear, is visible under Frank's short sleeve. (01:36:05)
Continuity mistake: At Frank's house, while Stuart rambles on about happy and productive ghosts, Frank pours himself a bowl of Jeepers Creepers yellowish color flake cereal. After Frank sprays Stuart in the face with the Shoo Fly, Frank eats cereal that are roundish dark-colored bits. (00:19:35)
Continuity mistake: The red marks on Frank's neck change in consecutive shots from the time he receives the injury. (01:29:30)
Continuity mistake: The colours on the dial of the freezer Frank goes in changes between shots. When Lucy turns it down you can see the colours are light and dark blue. Later on in the wider shots and when she tries to open the door and Milton Dammers stops her, you can see it's blue and red.
Audio problem: After Agent Dammers shoots Frank in the arm, in the close-up he shouts, "I don't want to shoot you in the back...I said turn around!" In the next close-up of Frank, Dammers repeats the latter, though nothing is heard. (01:36:20)
Other mistake: When Frank first runs into Ray's ghost on the street, and they duck into an alleyway to talk, Ray accidentally calls Frank (Michael J. Fox) by his real name "Mike" instead of his character name "Frank." Ray says "I felt this vise-like grip squeezing my heart, and I couldn't breathe, Mike."
Continuity mistake: At the police station, the filing cabinet beside Lucy is visible in the wide shot, just before Dammers says, "Debra's corpse had the number thirteen carved into its forehead." Then, in Lucy's close-up different things are on top of the filing cabinet. (00:46:10)
Continuity mistake: At Mrs. Waterhouse's home, the large potted tree, beside the doorway with the bouncing baby, is visible in consecutive shots and the leaves' position obviously differs in those shots. (00:22:55)
Revealing mistake: At the Excalibur Restaurant, when Ray's ghost gets angry at Frank he knocks over a wine glass with his hand. When the wine glass starts to tip over, the cloth under it moves and lifts up a bit to obviously tilt the glass towards Frank. (00:36:40)
Continuity mistake: At the police station, when Dammers tells Lucy about the day that Debra died, there is a shot of the utility knife in Frank's toolbox and the initials F.B. are written in white on the knife. Later, when Lucy finds Frank's utility knife in Mrs. Bradley's bedroom, the initials are written differently. (00:44:30 - 01:05:50)
Chosen answer: For the most part, the actors playing the ghosts were shot separately on blue-screens, and then comped into the scenes. (By removing the blue background through a process called "color keying", and placing them over the scenes) They were simply given a blueish glow and made semi-translucent to complete the effect. It was pretty cutting edge back in the 90's, but nowadays, it'd be very easy to make the exact same effect using a simple program like Adobe After Effects.