A nationwide manhunt for a convicted murderer would be led by a national agency such as the FBI or (as in the 1993 movie) the US Marshals Service, not by a local police lieutenant from Indiana.
The railroad car that Dr Kimble escapes from in the opening credits is marked Chemin de Fer. This is the name of France's railroad not an American railway company.
It is unthinkable that a convicted murderer would be transported to prison via passenger rail, in plain clothes, without handcuffs, with only one policeman to guard him. This was practically an invitation to escape.
Helen Kimble is shown in various flashbacks throughout the series as being beaten to death by Fred Johnson using the base of a lamp. Police would have found Johnson's fingerprints on it, and not Kimble's. But following this basic forensics procedure would have made this a single-episode series instead of four years.
Lieutenant Gerard knows that Kimble dyes his hair but every time his picture appears on a wanted poster or in a newspaper there is no mention of this, nor any attempt by a sketch artist to update his image to black hair.
Kimble throughout the series acts guilty every time police appear. While this would be the norm early in the show, his character would have developed an act so as to blend in with others, rather than standing out by looking guilty of something. His behavior is suspicious and would be noted by police officers quickly. To survive, he would have had to overcome this. However, he continues this behavior to the very last minutes of the series.
Lt. Gerard consistently tries to track Kimble down by himself or with only one other officer, which not only puts him in dangerous positions but allows Kimble to escape numerous times.