On Shoop's left hand, you can see that he has injured one of his fingers and it appears to have been smashed. This occurred when Mark Harmon had to actually put out the fire on the couch during the party scene that grew quickly out of control.
Carl Reiner arranged for the scene in which the students try to scare off a substitute teacher with blood effects and gory makeup on October 31st so that the actors could wear their costumes and makeup to the Halloween parties they were attending that evening.
The casting of Mark Harmon in the lead major role was the idea of director Carl Reiner. Reiner has said: "We originally discussed having a major comedian for the role. However Mark impressed me very much in the mini-series The Deliberate Stranger (1986) in which he portrayed convicted murderer Ted Bundy. When I saw him being interviewed on a news program, he was so personable and had such a winning smile that it was clear he would be well suited for the role of our gym-coach turned instructor. And he brings surprising depth to the character".
In the scene where Shoop teaches his students how to write a complaint letter, some of the lyrics to the James Brown song "Papa's Got a Brand New Bag" are visible on the blackboard at the front of the classroom. This is left over from a deleted scene in which Shoop diagrams (and sings!) the song for the class.