When Steve leaves in the middle of a football game to go home, there is light streaming through the front door's window and the porch is lit up as well. However, when he reaches the front door there is no light coming through the window in the door and the porch is darker.
At the first of movie Father Burke meets Steve Williams in the pool hall. When Father Burke racks the pool balls, the eight ball is in the incorrect position.
Tailback (number 11) throws his first pass left-handed, but his remaining passes are thrown right-handed.
On the first play from scrimmage versus Santa Carla, St. Anthony's pass was intercepted but the PA announcer said it was a fumble.
Steve Williams (John Wayne) makes the statement that President Theodore Roosevelt changed football rules and then was voted out in the next election. In fact, President Roosevelt urged that the rules be changed in 1905, and they were changed in 1906. Roosevelt chose not to run for reelection as President in 1908, despite huge popularity; therefore, he was not "voted out" in that election. Roosevelt chose William Howard Taft to be his successor, and Taft won the 1908 election. However, Roosevelt did not like the job Taft did and chose to run against him in the 1912 election as the nominee from the Bull Moose Party. Roosevelt split the vote with Taft, and Woodrow Wilson won the 1912 election. So, although Roosevelt lost the 1912 election, he was not "voted out" because he wasn't "in" at the time.
Steve (John Wayne), when scheduling his team to practice during the summer, states that he will have the advantage over Holy Cross, Notre Dame and "Santa Carla" (perhaps a fictitious version of Santa Clara), because conference rules prevent them from practicing during summer sessions. None of the three schools (assuming "Santa Carla" refers to Santa Clara) was ever affiliated with a conference in football. (Notre Dame eventually joined the ACC in all sports except football and ice hockey.)
At the start of the first game, the PA announcer says that Santa Carla will defend the south goal. The Polo Grounds was an East-West stadium for football.
During the montage of summer practices, the calendar pages do not match with one another. The first page has June 1 on a Monday and June 30 on a Tuesday. This means that July 1 should be a Wednesday, August 1 should be a Saturday, and September 1 should be a Tuesday. Instead, the calendar pages show July 1 as a Tuesday, August 1 a Wednesday, and September 1 a Thursday. And if September 1 falls on a Thursday, September 20, the date of the Santa Carla game, would not be on a Sunday as it is in the story.
When Steve throws the football at the window, several panes break without even being contacted by said football, especially those in the lower half.
Buck Holman (James Flavin) tells Father Burke (Charles Coburn) that Steve Williams was "kicked out of the game" a few years previously. However, he clearly says, "kicked out of the LEAGUE," and the change in audio is recognizable. Apparently, someone didn't want the Ivy League to have ever been associated with a coach of questionable character.
Camera shadow crosses Anne and Harold on couch just before Steve enters room and catches them in clinch.
Although the movie is set at a college in New York, there is a California flag flying near the stadium when Steve first meets the football team.
When Father Burke first announces his intention to solve the school's financial crisis, he says that his plan is in "Deuteromony" (rather than Deuteronomy), chapter 32, verse 15, a mispronunciation unlikely for a seasoned cleric. Additionally, when the others look it up, they read a paraphrase of an excerpt only, not the whole verse.
After overhearing them at the domestic relations court office, Steve refers to a mother and daughter in another case as "watermelon bottom and her daughter." The daughter was the one the kids called "watermelon bottom."