American flag with fifty stars shown in two scenes early in the movie. This story happened in 1956, when the U.S. flag only had 48 stars, as Hawaii and Alaska did not become states until 1959.
JB Peña and Frank Mitchell are identified as former Marines who served together in heavy ground combat action throughout the Allied campaign in Italy. In fact, no large Marine forces were ever involved in ground combat operations in Italy. Some 51 Marines served with the OSS in North Africa and Europe, and others served on board US Navy ships involved in the landing operations in the European theater.
When JB Peña meets with the head of the country club to try to join as a member, he introduces himself as the Superintendent of San Felipe High School. Later, when he meets the Principal of San Felipe High School, it becomes obvious that he should have said that he was the Superintendent of San Felipe School District, and he is correctly identified as such at the end of the movie.
When JB Peña first meets Principal Guerra in the parking lot, Guerra asks if he has any ideas for improving the high school's reading scores. Texas did not begin statewide testing for reading, writing, and math until 1979.