During the administration of the lie detector test, the window behind the examiner and Frank has an obvious prison yard background. Then, the camera angle shifts to a close-up of Frank and a clock-face within the room. The camera then pans back to the examiner. The scene in the window has changed to an English cottage by the sea with someone working in the fields.
When Jim wakes up after a rough night and goes to the living room and sits at the puzzle, he lights a cigarette with his right hand. When the camera changes and shots from the left from his wife's perspective, the cigarette is in his left hand. As the camera changes back and forth, the cigarette changes from his right to his left hand.
Continually throughout the film, McNeal incorrectly refers to Springfield and Joliet as "up there", when really these cities are southwest of Chicago. Then, when visiting Springfield, he incorrectly refers to Chicago as "down there" while Chicago is really to his north. This is the opposite of how Illinoisans would refer to these areas. Springfield and Joliet are south of Chicago and are always referred to as "down there" or, more often, "downstate," from a Chicagoan's point of view. When visiting Springfield, you'd go back "up" to Chicago. Illinoisans' terminology of "up there" and "down there" always respectively follow the north and south directions of the map. In addition, when Kelly says he stopped at the prison outside Joliet while on his way to Decatur, McNeal suggests this is just an excuse as Decatur is in the opposite direction; in fact, Decatur is in central Illinois, and Joliet would indeed be on the way there from Chicago.
It wasn't necessary to enlarge and actually see the date of the newspaper to determine the date of the issue. Since the layout of a newspaper's front page changes daily, and the front page was visible in the photo without high magnification, even if somewhat blurry it would have been sufficient to tell which day's issue it was when compared to archival copies, especially since the day had been determined to within a very small range of possibilities.
At some point in this film someone refers to Soldier Field as 'Soldiers Field' - a mistake that a Chicagoan would not make. However, there is a feature of Chicago neighborhood slang of adding an unnecessary possessive "s" to the name of local institutions: somebody going for groceries at the Jewel Food Store chain would say they were headed "by the Jewel's."
When McNeal first visits Tillie, he has no camera nor a photographer with him. The next morning, city editor Kelly is holding a paper with a photo of Tillie scrubbing the stairs. However, it is possible that McNeal sent a photographer back after meeting Tillie, since when he first met her he wasn't sure she was the right person.
The goof item below may give away important plot points.
It's highly unlikely that there would have been enough resolution in the original print to see a headline, let alone read the date on the newspaper. If there were, they would have been able to easily see the date with a simple magnifying glass. Only photographic enlargement performed on the original negative could possibly reveal additional small details. Instead they created a new negative from the print in order to make the enlargements. Since the new negative is made from the print, there is no way to recreate details that can't be seen on that print in the first place. If your original is missing enough legibility to see the fine details, no amount of copying or enlarging can possibly improve upon that.
Also, there's no need to read the date - in the first enlargement, probably, and definitely in the slightly larger second enlargement, it should be possible to identify the date from the layout of the newspaper page.