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: 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.
Continuity mistake: During the scene in the dam tunnels, Kimble holds Gerard at gunpoint. In the first close-up, Gerard has three strands of hair that are all apart from each other. The shot cuts to Kimble and back to Gerard, and the strands are all together. Then it goes back to Kimble, who says "I didn't kill my wife." When it goes back to Gerard again, the strands are apart once more. We know he couldn't have moved them because he has his hands up. Later, when Gerard is holding up Kimble at the tunnel opening, there is only one strand on his forehead.
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.
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.
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.
Visible crew/equipment: When Kimble is walking through town the morning after his escape from the bus, he passes by windows, and one shows a Steadicam camera man in the reflection.
Factual error: When Dr. Nichols leaves the damaged elevator, and Kimble later exits (the infamous arm in the door shot), neither would be possible as the elevator was emergency stopped by Nichols and can be seen positioned just below the floor. The elevator doors would not line up with the floor doors, and both sets would need to be manually opened.
Deliberate mistake: The dummies are obvious when the jail bus is flipping over onto the railroad tracks.
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.
Continuity mistake: In the flashbacks seen at the start of the film, Charles Nichols introduces Kimble to Alec Lentz. When this flashback is revisited later in the film, when Kimble breaks into Frederick Sykes' house, the words and actions of Nichols and Lentz are slightly different to what was seen earlier in the film. (00:04:15 - 01:24:55)
Other mistake: After the train crash the news crews and sheriff are interviewing the surviving corrections officer. He boasts how heroic he was to rescue his partner from the wreckage, claiming that he was his partner and he would do the same for him. The only problem is that they are surprised when they find that same surviving corrections officer several scenes later and rush him to the hospital. Why would they be surprised to find an officer they already knew about?
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.
Factual error: When Kimble is being interviewed by the police, a cop says "book him." We later learn the police were still trying to find out if a one armed man could've done it. The police can't arrest someone if the investigation is still ongoing. An arrest is supposed to mark the end of an investigation, the trial is the next stage.