More or less any time Annie Hacker appears, there's a 50-50 chance of Jim proving his humanity in a way most life-affirming.
Jim getting tearful when he gets it into his head that Sir Humphrey is dying.
When Humphrey puts down the phone at the end of "Party Games", Hacker, in an agony of uncertainty, asks him "Is it...?" and points more or less at himself. Humphrey, who has been stone-faced throughout the phone call, suddenly smiles at him like a proud dad, and says respectfully "...Yes, Prime Minister." Turns into a Crowning Moment of Funny as Hacker, feeling destiny call, stares nobly into the middle distance and unconsciously slips his hand inside his jacket like Napoleon.