LOS ANGELES—In a nondescript building attached to an outdoor mall, Joan Graves and her colleagues sit down each day to talk about the movies they have seen. Nothing unusual there.

In this office, though, nobody cares about a film’s Academy Award prospects. Their reviews focus on a different set of criteria: Did any ashtrays appear on screen? When the bad guy got shot, did his blood ooze out slowly or splatter against a wall? And just how “active” were the actors during their romantic interludes?

One...