When Biegler returns to his house at the start of the film, McCarthy points to the United States Supreme Court reports and asks if they should read "a little Chief Justice Holmes", and Biegler also refers to "Chief Justice Holmes". Oliver Wendell Holmes was an Associate Justice of the U.S. Supreme Court, never Chief Justice. (He was, however, Chief Justice of the Supreme Judicial Court of Massachussetts before being appointed to the U.S. Supreme Court.)
When McCarthy is driving back at night, his car is shown approaching a fork in the road, with a large white sign in the area where the road divides, and taking the left-side (from the driver's viewpoint) fork. The shot immediately shifts to McCarthy in the car, driving, squinting ahead, passing other cars whose horns are heard and headlights seen. The scene then shifts again, back to the very same shot of the car approaching the same fork in the road, even though by then the car would have been well beyond this area, having already passed it several moments earlier.
Several times in the movie one of the characters makes a humorous comment and you hear the courtroom audience burst out laughing; however, when the camera immediately turns to the audience, they are shown completely still and without emotion.
Lt. Manion and later Dr. Smith are shown arriving from Detroit on the Chicago and Northwestern Railway. Such a trip would have meant traveling via Chicago and changing trains (and stations). The trip, depending on connection times, would take well over two full days each way.