Mr. Cleary uses the term "quantum leap" in its modern sense, meaning a large increase. Dictionaries put the first use of the term, as opposed to its original scientific sense, in the late 1950s or early 1960s. It's very unlikely that a French teacher in the 1950s would use it that way.
During the introductory scene in David Green's room, when Van Kelt grabs McGivern from behind and administers a noogie, McGivern elbows Van Kelt and escapes his grasp, leaving his overcoat in Van Kelt's hands. He then darts out the room. In the next cut, a long shot from down the crowded hall, McGivern waves his overcoat over his head as he runs away from the room and Van Kelt chases him.
David is right-handed. From the receiver's point of view, the ball should rotate counter-clockwise when he throws it. At the end of the first game against Winchester, the last two shots of David's game-winning touchdown pass, from the receiver's point of view, the ball rotates clockwise.
When David is having dinner with the Dillons, Mr. Wheeler is introduced to Tom Keeting, who is wearing glasses. When he is about to sit, his glasses disappear. When he is sitting in chair, his glasses are on.