During the argument scene between Sarah Brady and Rachel Brown (at around the 1:49 mark), Mrs. Brady's hairstyle -- specifically her bangs -- changes multiple times.
During the courtroom examination of Matthew Harrison Brady by Henry Drummond, Drummond shows Brady a 10 million-year-old rock, which he places on the judge's desk. Later in the scene, the rock is back in his hand, and when he dismisses Brady, he places it back on the desk without ever having picked it back up.
The signage on the buildings shown through the windows behind the judge's bench changes from day-to-day during the trial (i.e., the "hot and cold" sign).
During the street carnival scene when Drummond arrives, Spencer Tracy's tie knot change from shot to shot. Gene Kelly's makes a significant change during the monkey meeting scene. When the camera is on the stage with the monkey, Kelly's tie has a deep dimple below the knot that it did not have before, and then when the camera moves down into the crowd for the handshake with the monkey, the dimple disappears. Tracy's knot continues to flatten and move side to side, all the way through the approach by Royce McHenry, and as they finally walk up to the high school boys, his collar is even flipped.
After Drummond excuses Jessie Dunlap from being a juror, he walks back to his chair and sits down. As Drummond and Brady are viewed from the back, he is sitting right next to Brady, not where he is supposed to be which is on the other side of the courtroom with enough space between them for people to walk up to the witness stand. Looking at his position with respect to the judge in the background, it is obvious he is sitting on the left side of the courtroom, not on the right side.
During the argument scene between Rachel and Mrs. Brady, Mrs. Brady slaps Rachel on the left side of her face. Rachel sits down and touches the right side of her face, not the left side. Actually, she's rubbing the tears from underneath her right eye, not rubbing her cheek.
When Drummond is inquiring about the story of Jonah, he flips to a book mark towards the end of the Bible and opens it. The Jonah story is in the Old Testament, but the section Drummond flips to would be towards the end of the New Testament.
On several occasions a wrinkle is visible in Fredric March's bald cap. Also, in closeup, the glue used to adhere hair to his head can be seen near the hair line.
When the Bradys walk toward the hotel porch after the revival meeting, the lights and buildings of the town are seen behind them. When Drummond leaves Brady on the porch a few minutes later though, the scene behind them, facing the same direction, is completely blank beyond a few bushes.
As Matthew Brady ends his arrival speech to a crowd of supporters on the street, the "(Give Me That) Old-Time Religion" is sung by the throng, but the extras following behind the car are either completely out of sync with the song or they are merely mouthing along with the singing because they don't know the words. Some of the extras are not singing at all.
(at around 1h 7 mins) Henry Drummond refers to latitude and longitude and states "minutes, degrees, and seconds". Though technically correct, it is unusual for people who are familiar with such to list in that order; typically, logically/mathematically when listing such, degrees, minutes, and seconds are stated as "degrees, minutes, and seconds" because that is descending/hierarchical order.
The jury can be seen talking amongst themselves during the trial; the judge should have admonished them not to do so until all testimony is complete and they retire for deliberation.
The film is set in 1925. During Drummond's cross-examination of Brady, he uses the word "sex", not to mean "gender", but as a shorthand for "sexual intercourse". The first known example of this usage was not until 1929.
E.K. Hornbeck (analogous to H.L. Mencken) calls the town "the buckle of the Bible Belt". Although this was one of Mencken's signature phrases, he did not start using it until 1926, one year after the events depicted.
During the voir dire phase of the trial concerning jury selection, Henry Drummond is forced to use his limited number of peremptory challenges to disallow prospective jurors who are obviously not interested in being impartial in any way to the point where one likens Prosecutor Matthew Brady to God. In that situation, Drummond should have called for such obviously biased prospective jurors to be struck for cause, a motion that can used an unlimited number of times with the permission of the court. If the court, which itself has obvious signs of partiality itself in the story, had rejected such a motion, Drummond could have resorted to using his peremptory challenges.
While Archbishop Ussher did theorize the time when the earth was created, the time and date that Brady quoted was by Dr. John Lightfoot, not Archbishop Ussher.
When Henry Drummond tries to call several scientists to testify on Darwin's theory, Brady objects to the introduction of "scientific testimony" in the trial, yet it was Drummond himself who earlier introduced such testimony when he asked the student witness to recount what his teacher told the class about Darwin's theory. Drummond should have objected on the grounds that the prosecution already had opened that door.
While questioning Matthew Harrison Brady on the stand, Henry Drummond refers to Charles Darwin's book as "The Origin of the Species". The book's title is actually "On the Origin of Species" (or, more popularly, "The Origin of Species").
When questioning Brady, Spencer Tracy's character says ".... Would you throw out the law and everything from Joshua to Revelations period?" There is no book in the Bible called "Revelations". The correct title is "Revelation".