* Sir Humphrey has one near the end of "The Moral Dimension" -- Hacker tells Sir Humphrey and Bernard that he intends to blow the lid on the corruption involved in a massive contract between the UK and the Arab state of Qumran, along with telling the press about how Bernard forged a valuation certificate so that Annie could keep a rosewater jar that she wouldn't otherwise have been allowed to hold onto. Even though it will likely destroy both the contract and the UK's relationship with Qumran, Hacker goes on a speech about how it's the moral thing to do, and therefore the right thing. Sir Humphrey seemingly agrees with Hacker... and then matter-of-factly asks Hacker which one of them will tell the press about the "Communication Room" (read: Alcohol Smuggling Room) that Hacker set up in the Qumran royal palace earlier in the episode, completely demolishing Hacker's position in the blink of an eye.
** Then becomes a CMOA for Hacker, as he has to completely make up a plausible story to tell a journalist with no time to prepare. He successfully manages to answer or deflect all the questions, to the point that even Humphrey says it was "superb". Now, if only he could display that level of savvy and cunning at other times...
* In a meta-sense; you know all that SesquipedalianLoquaciousness that Sir Humphrey was constantly doing? Those long, convoluted, complex speeches? ''Nigel Hawthorne memorised them''. And could still repeat some of them several years later.
** Another meta-moment: The opening title sequence was not just hand-drawn by Gerald Scarfe, but they were not animated with separate drawings. Scarfe had to draw with a camera in his other hand and take two pictures in-between brush strokes, and these pictures became individual frames in the animation. That is extremely difficult to do with any sort of accuracy, much less the kind of accuracy you see in the title sequence.
* Hacker's decisive victory over Sir Humphrey in the ''Yes, Prime Minister'' episode "The Key" is the culmination of a brilliant piece of farce and amazing acting from both Paul Eddington and Nigel Hawthorne.
* Hacker's first real, unqualified, triumph over Humphrey was in "The Skeleton in the Cupboard" when Hacker realizes he ''finally'' has leverage to get Humphrey to do the right thing and mercilessly exploits it with undisguised glee.
* While all Sir Humphrey's schemes are impressive, and several prove just how brilliant he really is, its hard to argue the one he pulls off in "The Bishops Gambit" isn't his masterpiece. In an attempt to assure himself to the cushy position of Master of Ballie College after he retires from the Civil service, he has to deal with the Dean who doesn't like him. Humphrey takes advantage of the Dean's love of Islamic culture and a diplomatic incident of a British nurse being sentenced to a draconian punishment in Qumran for a minor crime. Humphrey first sets up a XanatosGambit of having the Dean given the idea to negotiate for her sake, as a sort of interfaith meeting, as if he succeeds it will make him a candidate for A bishopric (which will certainly get rid of him) and if he fails he probably won't come back. He then also engineers it so Jim supports the Dean's trip, while quickly working to make sure the Prime Minster doesn't pick any other candidate as Bishop while he's gone. After the Dean succeeds in negotiating the Nurse's freedom and is hailed a hero, through a quite impressive period of manipulation and XanatosSpeedChess, Humphrey manages to engineer it so everybody (the Prime Minister, the Foreign Office, the Church etc.) comes out looking good from this, while leaving them with no idea he was behind it all, and at a loss at what his possible motivation would be, as how could he benefit from helping someone who didn't like him?
* When Hacker finally gets one over on Humphrey and the bureaucracy at the end of "Big Brother."
* From time to time Hacker gets one over on Humphrey, but it's often when Hacker is the one doing the wrong thing and Humphrey is the one trying to do what's actually in the national interest. In "A Victory for Democracy," Hacker finally not only gets one over on the bureaucracy, but does so in the process of winning a major foreign policy victory that's actually good for Britain and the world. The title of the episode is a DoubleEntendre, but it is not at all ironic: Hacker really does save democracy on St. George's Island while also winning a victory for democratic influence over British foreign policy and avoiding a war.
* Any time Hacker and Humphrey are forced to cooperate with each other, such as in "The Bed of Nails", when they figure out a way to get rid of the unwanted responsibility of creating a national transportation policy by deliberately choosing the PM's own constituency as a place to review the local implications. The combination of Humphrey's procedural know-how and Hacker's political instinct is devastating, and makes you wish they'd done it more often.
-->'''Hacker''': This is commuter country, isn't it? What about that?
-->'''Appleby''': Well--commuter trains run at a loss, you know. They're only really used at rush hour. So, commuters are in effect subsidised.
-->'''Hacker''': [''frowning''] Isn't that rather unfair on the others?
-->'''Humphrey''': Oh, it's a ''great'' injustice, minister.
-->'''Hacker''': [''to Bernard''] Commuters to pay full economic fares.
-->'''Humphrey''': [''actually looking slightly shocked''] Mind you, that'll double the price of the tickets, minister.
-->'''Hacker''': Can't make an omelette without breaking eggs. [''Humphrey nods thoughtfully'']