Fredric March's whole performance as Hyde. The book describes him as being "pure evil" and March makes you believe it.
Hyde terrorizing Ivy psychologically and emotionally. It's even worse because people do act like that in real life, and it's decidedly terrifying how quickly Hyde destroys her personality.
Jekyll's agonized faces as he first turns into Hyde. The Hyde makeup itself gets progressively more deranged as the movie goes on, with the final scene having makeup so corrosive it almost ruined Fredric March's face in real life.
The first transformation into Hyde has a moment of understated horror, as it immediately becomes clear how much of a mistake Jekyll has made. What's the first thing Hyde says when he comes into being?
"Free! Free at last!"
At one point Ivy is celebrating her liberation from Hyde, having received Jekyll's promise that she'll never see him again (and Hyde's promise that he'll kill her if she disobeys him). Then, just as she's toasting Jekyll, the door opens and Hyde walks in...
The bizarre closeups near the start of the film and the segments shot from Jekyll's perspective throughout the film can be this for some, largely thanks to just how uncomfortably close the people's faces are and the surreal, gauzy filter. This sets up an uncomfortable feeling in the audience for later on.
