Continuity mistake: In the climactic boat scene when Kevin Pollack runs back from the boat to the van full of money he shoots the man standing by the back of the van. Pollack is then shot in the back as he looks at the money in the back of the van. When Kevin Spacey returns to the van later in the boat scene, we see Pollack's dead body lying on the ground behind the van, however the dead body of the man who Pollack killed has disappeared.
Factual error: When the Suspects planned to kill Kobayashi, they waited for him in the office building. McManus got into the elevator and waited for the three men, hidden in the roof. After Kobayashi and the two men got into the elevator, and the lights went out, McManus fired twice. The blood on the wall behind Kobayashi would be correct if the two shots came from in front of the men. But McManus fired from the roof of the elevator, meaning the blood spray should be much lower on the wall and angled sharply downward.
Visible crew/equipment: When Verbal drops the Zippo lighter in the police office, Chazz Palminteri leans down to pick it up. When he leans down out of frame, there are 2 "C-stands" visible in the background. These shiny, adjustable stands are general-purpose utility holders on a movie set, used to position lights and light control material for a setup (i.e. flags, scrims, diffusion, etc).
Continuity mistake: Early on in the movie at the start of the interrogation between the cop and Verbal Kint, Kint asks for some coffee. A bit later on we see the contents of Kint's cup empty, then the camera switches back to the cop then back to Kint, showing that he has a full cup of coffee.
Continuity mistake: When Kobayashi first meets the Suspects, Fenster is laying on a sofa with his feet up on one of the armrests. Kobayashi says, "Mr. Fenster I recognize from his mug shots," and Fenster swings his feet down and sits upright. Thirty seconds later, Kobayashi says, "I work for Keyser Soze," and then Fenster swings his feet down from the armrest and sits up for a second time.
Continuity mistake: When the suspects are put into a jail cell together after their interrogation, Keaton walks into the cell. He is wearing his suit jacket in the shot where he walks through the cell door, but in the next shot, where he walks to a bench to sit down, his jacket is now slung over his shoulders.
Continuity mistake: During the line-up Keaton is holding his jacket folded over his left arm and covering his face with his right hand. When the turn comes to Fenster, from one shot to the next Keaton's jacket is folded over his right arm, and his right hand is covering his face.
Continuity mistake: Near the end, when Agent Kujan realizes who Soze is, he drops his coffee cup and it breaks in slo-mo. If you look closely, you can see that the bottom of the cup does not have the red writing on it. (I will not give away what the red writing is, as it may be a spoiler).