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)
Continuity mistake: After the bus crashes, Kimble unlocks his hands and throws the keys onto the floor in front of Copeland. Two shots later the keys are lying in a different position when Copeland grabs them off the floor.
Continuity mistake: When the landlord's son is arrested, it's snowing, and the following scene is during the St. Patrick's Day parade, with no snow on the ground. The only other time there was snow was when the other fugitive was arrested/killed, so they must have filmed that the same time of the year.
Continuity mistake: Kimble puts the worker's uniform on over his prison uniform, but when he takes it off to tend to his wounds, we only see him remove the worker's uniform, with no sign of the prison uniform.
Continuity mistake: When the Marshals go to arrest Copeland, they are in Whiting, IN. When the Sheriff's car comes through, it is an Illinois State Police car.
Continuity mistake: The prisoner starts foaming at the mouth and pulls the sharp implement from his sock, but when he is shot, he collapses back in his seat with no sign of the foam around his mouth.
Continuity mistake: When Kimble leaves the hospital and the detectives arrive, it's dark outside. However, when they're interviewing the nurse, you can see it's daylight outside.
Continuity mistake: When Kimble is on the moving train, Sykes mysteriously appears from a door when he wasn't there before. (02:00:00)
Answer: It's a cold compress. You squeeze it, and the inner bag breaks mixing chemicals and it gets very cold. It helps to minimize swelling. He gave it to Kimball for all the bruises he had.
Grumpy Scot