In the opening murder, the gunman is not wearing gloves. After the shooting, he is shown in close-up wearing gloves, dropping his cigarette. Then during his escape, while in shadow, he is visibly no longer wearing gloves. (Audio commentary reveals the close-up hand to be that of composer/editor John Ottman).
During the lineup scene, as Fenster reads the card, Keaton's right hand is over his mouth (trying to cover his laughter, see Trivia) while his left hand underneath his jacket. As the angle changes, his left hand is now on his face and his right hand is under the jacket.
In the scene where Kobayashi is walking through the office building flanked by his two bodyguards, just before the camera pulls back to reveal Hockney, we see an African-American woman in a white blouse and tan slacks walking along side of Kobayashi. In the next cut to Kobayashi walking through the elevator corridor, if you look to the bank of elevators to the left, you'll see the same woman coming out of an elevator as if she had just come down from one of the upper floors.
When the two police officers pick up the emerald smuggler at the airport, their squad car number on the license plate is 2485. Later when they are hit from behind by the van and are robbed the the squad car number on the side has changed to 6423.
In the scene when the men go to ambush Mr. Kobayashi at his law offices, just after he enters the front door of the lobby with his bodyguards, crew members and lighting stands are visible in the reflection of the polished marble as the camera dollies past the column.
After the lineup scene when the characters are moved to the cell, as Fenster begins to pace back and forth, there is a silver microphone visible underneath the bench that Todd Hockney is laying on. Two seconds later it vanishes.
When the police taxi service picked up the smuggler, after they were shown crossing the Verrazano Narrows Bridge, the smuggler handed the police the envelope of cash and asked if it was enough to get him to Staten Island. Having crossed the bridge, they would have already been in Staten Island. If they came from Newark Airport, they would have already been on and left Staten Island, but this wouldn't be the case as the New York City police would not have picked him up in Newark, New Jersey.
In the hospital scenes in the burn unit, the medical staff are gloved and gowned but their surgical masks are pulled down under their chins. Their masks should be covering their noses/mouths because burn victims are extremely vulnerable to infection.
In the opening scene when the police arrive to the dock of the burning ship, there are bodies lined up up on the pier covered in body bags labeled "S P CORONER" as in San Pedro Coroner. The Department of the Coroner is a function of Los Angeles County.
At the opening of the film we see some injured guy lying on the ship desk and someone shooting him from just 2-3 feet away. At the end, when the story is being re-enacted, the shooter is at least 12 feet away. However, this is entirely possible as the first time the scene is shown it is implied that it is actually happening; whereas the second time, towards the end of the movie, is a retelling of the story by Roger "Verbal" Kint.