After Richard Kimball first escapes they say he is near Route 15 and Interstate 57 heading towards Berkeley Dam. All these places exist, but Berkeley Dam (Kentucky) is around a hundred miles away from these two roads (Illinois), and besides, Berkeley Dam looks nothing like what they show in the movie.
When Kimball is jumping out of the back window on the train, the first view is from inside the train facing the back. He is the only person standing in the car towards that end. He kicks out the window. From an outside shot facing the rear of the train they show Kimball jumping out of the window. You can see another figure in the back window helping him out the window.
Kimball runs out the Grand Ballroom and ends up in the Presidential Suite in another fight. The doors he goes through out of the Ballroom actually lead into the Foyer for the Continental Ballroom, both of which are on the second floor. That Presidential Suite is on the 27th Floor.
Kimball has just finished talking on the phone with his lawyer when the cops hear the noise in the background. They figure out the sound is that of an El-Train. They then start to list the different places that have an El. One of the cities they name is Milwaukee - there has never been an El-Train there!
When Kimball jumps from the dam, the falling body is clearly a dummy, otherwise he broke every single bone in his body before he even jumped.
After Kimball 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.
When Tommy Lee Jones has found out that Kimball is in "the presidential suite" he turns the car and goes to the hotel. If you look at the way he is turning the wheel compared to in what direction the car actually moves you will see that it doesn't fit - the car turns around to the left but the wheel is turned to the right.
In the scene where Harrison Ford is being chased out of Cook county Jail, he tries to get lost in the St. Patrick's day parade. He takes his tan rain coat off, having a blue shirt underneath so that he will look different. Notice that when he takes his coat off in the middle of the parade, the next shot shows him having absolutely no coat.
When Richard Kimball and the one armed man are fighting in the train and when it goes outside of the train and it shows the one armed man stumbling backward it shows his "prosthetic" hand grabbing for the pole.