In one episode, a mole steals a gas that causes adults to mentally revert to their childhoods, then pretends someone else took it and used it on her. She does this by skipping rope and babbling about how much she loves watching Captain Kangaroo. Max figures out she's faking it because Captain Kangaroo wasn't on when she was a child.
One time, KAOS frames Max for armed robbery and murder by having one of their agents wear a lifelike Max mask for the robbery. Max is tried and convicted but manages to escape. He tracks the imposter to a cheap motel, narrowly avoiding the police, who then surround the motel. Max tells the imposter the motel is surrounded by CONTROL agents, tricking the imposter into putting on the Max mask. The imposter rushes out, is killed by the police... and the real Max steps forward and removes the mask, proving his innocence.
For a rare physical display of awesomeness from Max, see the Sword Fight in the climax of the Season 3 episode "The King Lives." You won't be able to watch it without saying "Let's Get Dangerous!" in your head.
Max gets 2 in "The Spy Who Met Himself." First, he fights off two KAOS agents singlehandedly (three if you count the double of Agent 13 he knocked out with a locker door), beating them and escaping (he wouldn't have been caught at all if the double of the Chief hadn't tricked him). Later, after Siegfried locks him in a Gas ChamberDeath Trap, he calmly uses all the little spy gadgets on him to pick the lock on his handcuffs, filter the air so he can breathe, and remove the bars from the window to escape.
Max also performs a successful Sherlock Scan during Siegfried's Fake Defector scheme, saving all the Chiefs of CONTROL from being kidnapped. Even Siegfried himself is impressed.
Her Day in the Limelight "And Only Two 99" is, unsurprisingly, full of these. First, she recalls how she gave the woman who came to kidnap her a black eye. They still got her, but she managed to escape without them even knowing she got away. So she goes back without them even knowing she was ever gone so she can figure what their plan is. When she finds out, she escapes by pulling a Wounded Gazelle Gambit and arrives home in time to stop her imposter from fatally poisoning her husband. The imposter attacks the Chief when he tries to arrest her, but 99 knocks her out with one punch. Whew, that was a mouthful!
99 also saves the day in "The Day They Raided The Knights," when she's put on leave due to budget cuts at CONTROL. She uncovers the KAOS munitions distribution point at her new job and manages to notify the Chief before she gets caught and tied up. When Max arrives, she escapes from the room unnoticed while still tied up to warn him what's going on, and gets back in time to knock out the woman who was about to shoot him — again, still tied up.
The Chief: You're going to get a commendation for this, 99. I don't care what the computer says, you're going back to work!
Rosa La Costa in "Pheasant Under Glass": Max and 99 get into a KAOS mansion undercover as an opera singer so she can sing a high C that will break the unbreakable glass cell where a professor is being held captive in the basement. However, after she sings the note, they go down to the basement to find the glass booth still completely intact. So what does she do? "I promised CONTROL I would break that glass, and I'm going to break it! Step aside!" She then runs at the booth, knocks it over, and breaks it with her bare hands.
"Tequila Mockingbird" opens with CONTROL agent Esperanza brawling with a KAOS agent in a bell tower, winning, and escaping with the MacGuffin artifact of the episode. She's killed shortly after, but not before she manages to hide the artifact and leave clues that would later lead Max and 99 to its hiding place. It's easy to see why everyone says she was one of their best agents.
Agent 86: Would you believe, in the piano?
Also at the end, where Dhalip, having since befriended Max and taken too much of Siegfried's shit, punches him out the car and into the river, with The Dragon remarking upon his hangtime.
At a point of the film where we know Max is a great analyst but are still unsure whether he's a competent agent or just a bumbler, he and 99 are cornered by an armed henchman, when 99 kicks a machine gun lying at her feet towards Max, and in one smooth motion he catches it and gives the henchman a single bullet through the heart. And he does it as though it were nothing.
More impressively, there's his escape from a CONTROL holding cell. Not only is his plan clever and pulled off skillfully, it involves getting beaten by a pair of guards. Yes, it is part of the plan that he gets a beating. Then once he's escaped he has the sheer guts to go and deliver his crucial information directly to the chief of CONTROL — that is, the man from whose cell he just escaped.
The moment where Max convinces Dalip not to kill him and 99. By giving him relationship advice.
The moment where The Chief finally gives the Vice President the beating he's "been waiting since Nixon!" to give.
And then when the Chief slugs a Secret Service agent who makes the mistake of being a bit snotty towards him: "Speak up, son. I'm an old man, you know."
Max gets one earlier, when he fends off what he thinks is an invasion of the base with little but a fire hose and a fire extinguisher. Sure, it was just his fellow agents, but that doesn't make it any less awesome of a plan.
Agent 99 is being held captive by The Mole, handcuffed to the support handle in the backseat, and making things difficult for him:
Agent 23: [after 99 kicks his pistol out of the car] See, this is your problem! Some men like women who are feminine!
Agent 99: [disbelieving outrage] What, I'm not feminine?!
[Kicks him in the face — from the backseat of the car]
Max finally getting in the classic car (only to immediately run out of gas), followed immediately by Bernie Kopell's cameo.
Carrell's Max driving the iconic Sunbeam Tiger heroically out of a freaking building, theme music blaring behind him. (And incidentally, Kopell is driving an Opel GT, Max's season 5 car, as a VW Karmann Ghia (Max's car in all but the opening in seasons 3-4) passes behind them. Continuity Porn FTW.