(At around 34 mins) When one of the guys, robbing the corrupt cops, wearing pantie hose on his head and sitting in the driver seat of the white panel van looks back and says "hurry up" and his mouth is not moving.
After Verbal shoots the smuggler, Keaton opens the car door, takes the briefcase, and closes the car door with bare hands, leaving his fingerprints behind. Having been arrested before, his fingerprints would be on file and he wold have been quickly identified as having participated in the murder. If Keaton was the smart, seasoned criminal he was made out to be, he would have been more careful and not left his fingerprints behind.
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.
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 scene of Saul's holdup, the angle of Keaton's gun changes between shots. When shown from Saul's right, Keaton is seen holding the gun at a downward angle. But in shots to Saul's right, the gun is level.
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.
(at around 12 mins) 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.
In the robbery of "New York's Finest Taxi Service", it is implied that Internal Affairs division fights corruption. However, in real life, NYPD IAD is equally likely to cover for "New York's Finest Taxi Service" as the ring itself.
During the line-up scene, as the suspects enter the line-up booth, a microphone can be seen above Hockney's position. This is a standard feature of police line-up booths. (In some releases of the movie this is not visible because the scene has been cropped vertically to change its aspect ratio.)
The robbery of New York's Finest Taxi service is a 5-man job, done with four vans, two of which have passengers not in the driver's seat. The van in front is driven by Keaton with Verbal holding the gun when the back door opens. The van behind rear-ends the car and gunmen hold guns on the cops from the driver's side of the van on the right and the passenger side of the van on the left. Who is driving the van on the left? Three guys (Fenster, McManus, Hockney) are doing four jobs (driver rear, driver left, passenger left, driver right). It's possible Hockney (in the left van) threw it into park and quickly slid over to the passenger window. But this is Verbal's version of the story, not necessarily what actually happened. It is quite possibly his mistake, not spotted by Kujan, rather than a mistake by the filmmakers.
When Kobayashi enters the lift with his two bodyguards, Macmanus shoots them. In the next shot we see that Macmanus is sitting on top of the elevator. But the blood of the two bodyguards splashes on the elevator window which in fact should have splashed on the ground since the shots came from above.
It can be argued that the blood splashed in all direction and hence came on the window, but Kobayashi who is standing just next to those bodyguards doesn't even have a drop on him.
The goof item below may give away important plot points.
Incorrectly regarded as goofs
At the opening of the film Keaton is shown lying on the ship deck and someone shoots 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.
When Verbal is being physically harassed during his interrogation he shrugs off the detective with his left hand but his left hand is supposed to be paralyzed. We find out later that he's faking his palsy.