Revealing mistake: During the St. Patrick's Day parade, Kimble removes his coat. In the next scene, he hasn't got the coat anymore, and he HASN'T dropped it. Don't be fooled. If you look to his right in the scene just after he takes it off, you can see a man carrying a coat that is the exact same colour and design. I assume this guy is supposed to be hiding the coat from view, but you can plainly see it. The guy is wearing a green hat. Kimble had no time to give it to him before the scenes changed.
Continuity mistake: In one scene, the ambulance is clearly marked FDNY even though the action takes place in Chicago.
Visible crew/equipment: During the chase scene in the access tunnels under the dam, there are several shots where the camera is in front of Harrison Ford moving backwards, showing him as he runs from Tommy Lee Jones. You can see the tracks that the camera dolly is riding on.
Deliberate mistake: The dummies are obvious when the jail bus is flipping over onto the railroad tracks.
Other mistake: When Dr. Nichols hits Dr. Kimble with a chair, look carefully. As Dr. Nichols swings the chair, it starts falling apart before it even makes contact with Harrison.
Revealing mistake: When Kimble jumps from the dam, the falling body is clearly a dummy, otherwise he broke every single bone in his body before he even jumped.
Continuity mistake: When Richard Kimble comes back to the hospital and is seen by the nurse, they embrace. There is a shot with him facing the camera immediately followed by a shot of her facing the camera. Their arms have somehow magically changed positions from the original embrace.
Character mistake: After Kimble jumps from the drain pipe over the waterfalls, the scene goes to Gerard standing in the pipe telling his crew to leave, then they all leave without picking up Gerard's gun that Kimble threw down next to him.
Continuity mistake: Kimble dives from the top of the dam when Gerard traps him in the tunnel. But in wide shots of Kimble falling, there's no tunnel above the dam. (The tunnel scenes were shot in Chicago, but the location sequences were done at Cheoah Dam in North Carolina - which has no tunnels.).
Continuity mistake: The scene in which Kimball in Cook County Hospital takes Joel to the lift starts with Kimball looking at the boys chest x-rays. In the first shot Kimball is looking at the front side of it and in the second shot (with camera looking over his shoulder) at the back-side but he does not let the x-ray out of his hand between the shots.
Factual error: During the car chase that leads to the tunnel, there are several freeway signs pointing to Murphy, North Carolina, and the film is set in Chicago.
Continuity mistake: Just before Harrison takes his leap from the pipe in to the dam, Tommy Lee Jones tells him to put his hands up. When Ford puts them at head height, Jones then tells him to put them above his head. Ford does this from the far out shot, but when there is a close-up of his face, his hands are at head level. This occurs in a fraction of a second so there was no chance for him to move them.
Factual error: In the scene on the El where the cop gets shot, you can hear the train engineer saying, "Balbo, next stop"; this is also said later on the police radios, when they say there is an officer down at the Balbo station. Two problems: 1) There is no Balbo station. 2) Even if there were, the station they start from is at Lake street (looks like the main transfer station at Clark and Lake), and the train pulls out going north. However, Balbo is south of Lake street.
Continuity mistake: After Kimble escapes from the prison bus moments before it's demolished by a train, he steals an ambulance, is chased through the mountains by a police helicopter, is trapped in a tunnel, escapes by crawling through a drain and jumping from a very tall dam into a raging river. A very thrilling sequence, but he's supposed to be in Illinois, where there is no terrain remotely resembling this.
Plot hole: When Kimble is heading towards the dam driving the ambulance in the tunnel, his lane is empty in the wide angles, yet in the close-ups he is swerving the steering wheel violently as if there were cars ahead. This keeps changing back and forth. It adds up for tension, but it is totally ludicrous.