Continuity mistake: During the dinner with Lucy at the restaurant, Ray's ghost knocks over the wine glass and the wine visibly spills onto Frank's vest, yet, the vest is dry in the following shots. (00:36:40)
Continuity mistake: When Frank's car is on Ray's lawn, until he pulls away, the position of the garden hose and bits of picket fence lying around on the lawn differ in the consecutive shots. (00:06:30)
Continuity mistake: After Frank nearly collides with the truck, he crashes through Ray's fence. The breaks in the picket fence differ depending on the camera angle. (00:06:15)
Continuity mistake: When Frank is in Lucy and Ray Lynskey's house pretending to get rid of the 'persistent residue of the departed', things in their kitchen (floor, fridge, counter, etc...) appear/disappear and/or change position between shots. (00:13:40)
Continuity mistake: When Frank reaches the chapel he places the urn down and there are scattered pieces of wood hanging over the edge of the bench. After Frank breaks through some of the wood on the chapel door he causes the pedestal to fall over on the bench and the wood is gone. (01:34:55)
Continuity mistake: In the sanatorium, after Frank accidentally knocks over the statue outside the chapel, the pedestal falls onto the bench sending the urn flying above. In the overhead wide shot the urn flies upside down as it reaches the window, yet, in the next close-up the urn is right side up as it comes through the window. (01:35:10)
Revealing mistake: When Frank, and later Ray, are shooting the water pistol, in the majority of the shots nothing is actually coming out when something is supposed to be.
Continuity mistake: When Frank hacks away at the door of the chapel, the broken wood at the openings differ in the close-up of Frank's face through the door and the following shots. (01:35:00)
Revealing mistake: The scar near Agent Dammers's left eye changes shape and position throughout the film. (00:41:15 - 01:35:25)
Revealing mistake: A squib (a small explosive device) is seen on Frank's arm when Dammers shoots him.
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.
TedStixon