When "Richard" starts to limp it wasn't planned, Harrison actually hurt a ligament in his knee shooting a promo for the movie, a promo that wasn't even part of the movie. He refused to receive treatment until filming was finished and ended up needing surgery. See more...
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Continuity: 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: When Kimble is fighting the one-armed man on the train, the one-armed man shoots the metro-cop, then he and Kimble fight some more. Kimble knocks him out with his gun (silver). He goes to check on the cop, sees he's dead so he takes his cuffs and gun (black). He cuffs the one-armed man to the rail puts his gun (silver) into his right pocket, and the cops gun (black) into his left pocket, and then makes his escape. Later on, he dumps the guns into a mailbox, but he pulls the silver gun out of his left pocket, and the black gun out of his right pocket. The guns changed pockets before he dumped them.
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.
Other: After Kimble has been rescued from the train wreck and unchained, he escapes, running alongside a body of water. As Gerard announces to the other officers that there's a fugitive on the loose and gives instructions, Kimble is seen running again, in a replay of the earlier shot. Not only are all the same landmarks in place, but at the end of both sequences, he moves his arm to shake off a branch that's snagged him.
Revealing: When Dr. Richard Kimble is nearly run over by the freight train, look closely at the axles of the locomotive passing overhead. Diesel locomotives have large electric motors on each axle that actually propel the train. These electric motors are missing which would be similar to a car without a transmission. There is no way for a locomotive to move under its own power without these electric motors.