The phone call scene. No music, no effects. Just a fantastic screenplay and a powerhouse actor giving everything he's got and revealing a perceived monster to just be a broken man.
Jim Reston gets one in his first appearance when he tells Frost and co. how important this is and reminds us of what Nixon did with very believable anger, seeming incensed at the very notion of being sympathetic to him. It's the kind of emotional outburst Dr McCoy would have been proud of.