The moment in the pilot where Shawn convinces the police not to arrest him because he's a psychic, demonstrating his abilities to their astonishment and awe. What makes this moment particularly awesome is that he isn't one. It pretty much sets the scene for all the on-the-fly Refuge in Audacity moments he'll pull throughout the series.
Carlton tapdancing. Also counts as a Funny as... well... it's Carlton tapdancing as well as the fact that in the middle of the routine he has an epiphany moment and says out loud (while surrounded by children), "I know who the Westside rapist is!"
Shawn throwing the cell phone into the ocean in "An Evening With Mr. Yang." After running around following Yang's clues, Shawn takes control of the situation for the first time.
Doubles as heartwarming, but when Shawn hears that Gus is taken hostage, he stands for half a second comprehending it then immediately tries to rush in. Lassiter has to hold him back.
Tied to a chair, in a completely serious tone, "You kill him, I kill you."
The police have three suspects restrained around an inactive bomb one of them designed. Shawn tries to find who designed the bomb by activating it on a sixty-second clock, with two police officers restraining three suspects within a meter of it.
Gus is not the kind of guy you'd expect to have a CMoA; usually the nerdy Straight Man, he exists mainly as a long-suffering foil to the antics of his much cooler friend Shawn. Then, one of of their cases takes Gus and Shawn to a comic book convention where Gus meets a few people he pretends not to know, Shawn makes a few too many snide comments and Gus delivers a rant that not only even impresses Shawn, but will resonate with anyone who's had to put up with one too many people making fun of their interests:
Gus: [Discussing a sci-fi movie blog] Everybody reads this blog. Shawn: [Dismissively] No, not everybody. Gus: [Snapping]: Everybody here does, Shawn! And you know what? I don't care what you think! So why don't you let me do the talking here at the convention? And try not to embarrass me. This is my turf. And yes, I knew the guy in the codpiece. His name is Dave. And he's a really nice guy. [Gus swaggers off in a nerdy yet strangely cool fashion] Shawn: [Stunned speechless] ... Snap.
The unexpected moment in "Earth, Wind, and... Wait for it" where Gus and Shaun are suddenly thrown for a loop when the arsonist they're talking down sets a dangerous fire. Gus immediately takes charge, orders Shaun to carry out the unconscious Woman of the Week and dives for the arsonist, who'd just set themself on fire, saving them, and carrying him out in a rolled carpet (or something resembling it, at least).
In one episode featuring people recreating the Wild West setting in everyday life, obstructive Head Detective Carlton makes the arrest with several police cars behind him on a wide, dusty road. Because of the position, he and his quarry instinctively begin a standoff. Carlton proves he isn't all talk when he delivers the quicker shot.
The opening of "Shawn has the Yips" has one for Lassiter. The second Shawn tells him there's a guy with a gun, he goes Guns Akimbo on the hooded man, exchanging fire with him. Sure, he misses, but the fact that he carried guns to a baseball game...
"Shawn Takes a Shot in the Dark," is a crowning moment of awesome for almost the entire cast, but specifically for Shawn, who, over the course of the episode, escapes from the trunk of a moving car, jumps from one car to another during a high-speed chase, and uses a gun for the first time in the series to successfully hit a target both his ex-cop father and Detective Lassiter couldn't. However, the true CMoA for Shawn is when he uses his hypersensitivity to watch a bullet as it's fired at him. It still hits him, but damn!
That was actually the second time in the series Shawn fires a gun. The first is in the pilot, with the only witness being Lassiter's partner, who is replaced by Juliet in the second episode of the series. This scene establishes that Shawn is a crack shot as he fires through the bullet holes previously made by Lassie's old partner at the gun range. Which makes it a CMoA in itself and grants another one for setting up a bit and waiting 4 years for the payoff.
Also earns us this gem of a line, which coming from Lassiter is awesome in and of itself:
Lassiter: Nice shooting, Detective.
"If Shawn really has been shot, there's no room I'm not gonna bust open to find my son."
From "Mister Yin Presents", Lassiter gets one.
Lassiter: You have other units, chief. I'll be going to get my partner now.
Shawn also gets one when he steps up and does the responsible thing; "It's Jules; we know where she is, we follow Lassie, we save Juliette." Then he figures out the clue and saves Abigail.
And then his words to Gus as he sets out to save Abigail alone: "The only way I can't be there for Jules is if I know YOU are."
Gus gets an offsceen one in "Tuesday The 17th." Shawn and Juliet are tracking down a killer, who has ambushed Gus and some other victims while they were off looking. After finding out, Shawn spots Gus being attacked by the killer (who is wielding a knife) alone and immediately rushes in to rescue him. After running always to the scene he desperately runs to what he thinks Gus' collapsed body, only to find out it's the killer - Gus had already beaten him up off screen, without a scratch on him. Of course, then the killer wakes up, and it's him vs Shawn instead.
Gus and Lassiter's rescue of Juliet in "Mr. Yin Presents." Gus grabbing the hand of the clock, and Lassiter jamming the gears.
In "Last Night Gus", Shawn's speech about what it feels like to lose his Sherlock Scan and/or Psychic Powers that devolves into a deranged rant about convincing a child they've been given an ice cream cone. Which was apparently improvised by James Roday.
In "The Polarizing Express", an unnamed extra gets this with one line. The entire episode has been about the characters trying to bust the head of a gang on tax evasion, because they can't get him on anything else. At the end, Shawn jumps on a police car and gives an impassioned speech, with Gus, Lassie, and a one-off character joining in, until all the innocent bystanders are convinced to testify against him. The first person to agree was a young woman who was there with her daughter.
In "Shawn Rescues Darth Vader", Shawn successfully blatantly lies about being a pyschic on a lie detector. A Lie Detector that, considering in they're in fictionland, always work perfectly.
In "In for a Penny...", Juliet's father's plan to catch the thieves was essentially a reverse Trojan Horse. They arrested the getaway van driver, and Lassiter drove the van, with the heavily armed thieves inside, to the police station. They arrive and a SWAT team opens the back of the van to arrest them.
In Christmas Joy, Lassie ambushing and arresting the bad guy while dressed as Santa Claus.
In one episode where Shawn and Gus are working undercover on a minor league team, Shawn accidentally causes the game to dissolve into a massive brawl. Gus (the mascot), runs out trying to break it up, but one of the players punches him. Gus responds by drop-kicking the guy. Keep in mind he's dressed in a giant bird costume the whole time.
In the same episode, Gus as the mascot gets booed for his tap-dancing. Later, when he's firing a t-shirt cannon, a drunk heckler shouts "You can't dance for crap!" Gus doesn't miss a beat before shooting him with the cannon.
At the end of the episode Let's Doo-Wop Again, Lassiter and his girlfriend, Marlowe, are attending a concert in the prison. Throughout the episode, they've been having all their romantic moments interrupted by a joyless guard shouting "no touching!" When the concert dissolves into a riot, Marlowe steals a quick kiss, then hits the guard over the head with a chair!
Jules vs. Serbian assassins in Lassie Jerky. Jules wins. With a crossbow.
Shawn has several throughout the Season 7 premiere, starting with this:
Shawn: There’s one thing I’d like to do before we eat, though... let's catch the son of a bitch that shot my dad.
Juliet's "The Reason You Suck" Speech to her con-man father after realizing, based on a single sentence, that he was the one who stole a collector coin and planted it on the man they were interrogating to save face. Though there was a bit of Tear Jerker too in how broken their relationship was.