During the school bus scene, Chris Farley turning bright red in aggravation was improvised, according to Adam Sandler in I Am Chris Farley (2015). Chris, before filming that scene, downed six entire cups of espressos. He would do that in most of his other movies to maintain his trademark manic energy.
During the dodgeball scene, Adam Sandler hit the kids with the dodgeball as hard as he possibly could. The editor had to cut away quickly after each hit so that he didn't show the children crying.
Bradley Whitford never actually saw the film after it was released. But according to his brother, people would often shout "Business Ethics!," a reference to the scene where his character is challenged to discuss that as a subject.