When Alice goes to the bathroom cabinet, you can see the camera reflected in the mirror when she opens the cabinet door. It and the cameraman are hidden under a white sheet, with just the black, square lens showing through. (Freeze-frame recommended.)
When Alice is telling Dr. Bill her confession about the naval officer, the audio has her saying "you and I made love" while her lips move to say "we made love". In the context of the following sentences it's clear she was making love to Dr. Bill, but from the preceding lines her "we made love" could have ambiguously referred to her and the officer.
When Bill goes to the Sonata Jazz Club, outside the club is a poster of the four members of the band with their names. It lists Larry McVay as the drummer and Kip Fleming as the bassist. But inside the club, after the band is done playing, Nick (the pianist) introduces the band saying "Larry McVay on bass and Kip Fleming on drums."
When Alice and Helena are doing story problems, Alice says "Joe has two dollars fifty," which is a UK/Australian construction, as opposed to the more American "two dollars and fifty cents" or "two fifty".
When Victor Ziegler (Sydney Pollack) refills his and Dr. Bill Harford's (Tom Cruise) Scotches during their final conversation in the Red Pool Room, Victor switches glasses with Bill.
In the orgy scene, when Bill enters the room where there are several people on the long table, we see two people in cloaks (one standing and one sitting) obscuring the camera's view. In the reverse shot of Bill, these people are no longer there in the background. These people were added virtually in post production, following the death of Stanley Kubrick and the movie's subsequent NC-17 rating.
When Bill and Alice discuss her near-infidelity, the ashtray they were using when smoking the joint appears and disappears from the bed, the tapes and CDs are in different positions, and Bill's hand jumps off Alice's hip.
When Bill is going to the room where Marion is, we can see two tables in the corridor, with a sculpture on each one. When Carl arrives some minutes later, the sculpture on the first table has disappeared.
When Bill enters the temple, there is a laptop to the left of the pianist on a black box. From the other side we see the black box but the laptop is gone, only to return shortly after when we see him from the other side again.
In the orgy, the girls in the ring change places between shots: The ones to the left and right of the girl who eventually chose Doctor Harford leaves before her. When she is called to leave, there is suddenly another girl beside her.
When Dr. Bill Harford leaves Domino's apartment the second time after meeting Sally, her roommate, he is shown walking down a Manhattan street and passes buildings with numerical address 36, 37 and 38, all on the same side of the street. However, in New York City, even numbers are always on one side of the street and odd numbers are always on the other side. He could not have passed the street addresses 36, 37, and 38 on the same side of the street. In fact, an earlier scene on the same street shows an address 25 on the opposite side (shown when Dr. Bill Harford notices that he is being followed by a man).
Bill Harford arrives at Rainbow Fashions by taxi from the Sonata Cafe, and as he talks to Milich, Gillespie's Diner can be been seen across the other side of the street. Earlier in the story we discover that Gillespie's is next door to the Sonata Cafe, so there's no way he would have taken a taxi just to cross the street, (not even in NYC).
When Bill returns his costume to Rainbow Fashions, Millich tells him the bill is $375. His daughter then comes out and interrupts the transaction. When the Chinese men leave, the transaction has supposedly been completed, but Bill never actually paid.
When the nude masked woman walks up to Bill Harford with the masked man, in the first shot (with her hair behind her), she is one actress, but in the next shot (with her hair in front of her), she is an entirely different actress. One can easily tell this even though she is masked and naked.
The goof item below may give away important plot points.
In the mortuary scene, the attendant opens the drawer for Dr. Bill Harford to view the body. When the drawer slider comes to a halt, Mandy's breasts shake: the time line for rigor mortis would not allow this jiggling to occur.
The 3-column New York Post article "Ex-beauty queen in hotel drugs overdose" has two duplicated lines of type on the same row in all three columns, as though two identical articles had been cut and pasted together in the wrong spot.
When Dr. William 'Bill' Harford is reading his rescuer's obituary, two lines from the second paragraph of the first column 'Hotel by security personnel after her / agent asked them to check on her be-' are printed a second time before the following lines. There are also similarly repeated sentences in the second and third column as well.