At the beginning of the Mr. Julius Caesar contest at St. Benedict's, Sedgewick Bell is standing on the right and Louis Masoudi on the left, from Mr. Hundert's perspective. Later they have inexplicably switched positions, with Bell on the left.
When Sedgwick is finishing writing his final Julius Caesar essay, there are still a few pages of paper left in his yellow essay book. But when Mr. Hundert flips through the essay a moment later, every page is full of writing.
When Mr. Hundert exits the helicopter, the blades slow down impossibly quickly between shots.
As the boys are running into the building after Hundert breaks the car window with a baseball, a redheaded boy near Hundert drops his bat twice. Also, Hundert's green tie switched places as the boys were running.
After Mr. Hundert is startled by the slamming of books in his classroom, some of the chalk marks on the board change several times between shots.
When the students are caught on the brink of skinny-dipping, one of the nuns is wearing a wimple (traditional headgear and veil) together with a habit that has an above-the-knee skirt. You would never see a nun wearing such a combination.
When the girls are removing their shirts to go skinny-dipping, a Victoria's Secret Body by Victoria bra is revealed. That bra is from the time the film was made, not the mid-1970s when the scene takes place.
The boys are studying Latin using the first book of the Cambridge Latin course. The edition they are using is the third edition in hardcover, which wasn't released until 1988.
Sedgewick has an image of a smiley face with a gunshot wound in its forehead displayed in his room in the mid-1970s; the bloodied smiley face did not become popularized until the late 1980s.
The beginning of the movie is set in 1975, but there are '80s-model cars in the background.
Mr. Hundert misspells the word "republic" during one of the Julius Caesar tests.
Louis Masoudi's name is misspelled "Luis" in the yearbook next to his photo from the competition.
Mr. Hundert, a pedantic and demanding classics professor, would be unlikely to make the error of saying that Caesar's army was "comprised of" two legions. He would have said that Caesar's army comprised two legions, or that two legions composed Caesar's army, or that Caesar's army was composed of two legions. A trivial error, perhaps, but out of character nonetheless.