In the pilot, Holmes manages to deduce that the victim's psychiatrist husband is manipulating his patient, but is unable to come up with solid proof. After confronting the psychiatrist and receiving a Smug Snake response, Holmes takes Watson's car and smashes it into the psychiatrist's expensive coupe.
"While You Were Sleeping":
The Batman Gambit Holmes pulls at the end, which involves making up a fake heir to the family fortune and convincing a suspect that he's actually suspicious of someone whom the police have already cleared. Bonus points for staging an assault of a police officer and pretending to be arrested. Damn fine acting, Holmes.
A private detective, who was hired to trail one of the victims, refuses to reveal information pertaining to the case at hand. Holmes takes him aside, pretending to want to know about his office plant, and threatens to reveal the detective's meth addiction in front of Captain Gregson and Detective Bell, especially since the private detective is an old friend of Gregson. The detective then relents. Even more lovely, he's clearly sympathetic to the detective, and offers the name of the clinic where he'd undergone detox.
Joan realizing that her date was lying when he said he wasn't married.
In a group therapy session, a grumpy Holmes is mouthing off about how much he dislikes the therapy sessions. Watson, having learned that he puts himself into a trance from the last time they went, threatens to jab a thumbtack into his thigh to keep him awake. The Death Glare on her face wisely shuts him up. Bonus points as the line she used was an Ironic Echo from when Holmes was trying to determine whether or not the coma a suspect was in was real or not. "Lots of nerve endings there..."
In "Child Predator" Holmes finding a loophole in Adam Kemper's immunity deal: The deal specifies that Kemper cannot be prosecuted for any crimes committed while working with Samuel Abbott. Holmes, using Abbott's hospital records, is able to prove that Kemper committed one of the murders alone and therefore can be charged.
"Rat Race" gives Holmes two:
Since he hates Wall Street elites, he decides to wine and dine on their expense, having the time of his life. A notable moment is when he deduces that a man will propose and gives them expensive wine, which also counts as a Heartwarming Moment
Captured and held at gunpoint by the killer, Sherlock's about to die. He refuses to dig his own grave, and then when the cops arrive, distracting the killer, Sherlock picks his handcuffs, grabs the killer's taser, and turns the tables. This Holmes hasn't had as many physical moments as his literary or BBC counterpart, but this is a promising start.
In "Lesser Evils" Joan diagnoses a girl with a relatively rare condition through a minor foot injury.
In "Flight Risk" Joan deducing that Sherlock has a fear of planes, just through body language cues.
"The Long Fuse":
A minor one at the beginning, but Holmes is watching six television sets and reading a book at the same time...and can apparently recite the contents of any one of them at will. Even for Sherlock Holmes, that's pretty impressive.
Also, Holmes deduces that a bombing suspect is innocent based solely on the absence of an oak tree on a battery logo and an old picture of Barack Obama. Both of which prove that the bomb is four years old and thus, could not have been built by the suspect, who was in prison at the time.
The Eponymous M has knocked out and is about to kill a woman, when Sherlock confronts him:
"M": You! Sherlock: Me! Baton! [whacks "M" out cold]
Followed by a speech on how studies show how the average man will react to any situation, but he's not an average man. Followed by him stabbing M in the stomach, in the precise way that will avoid hitting any organs, to give himself an alibi when he turns M in to the police.
An offscreen one, for Moriarty. She fooled Sherlock Holmes. She fooled. Sherlock. Freaking. Holmes. Were it not for Moran mentioning his alibi, Sherlock would probably be in jail.
And another for Watson's growth as an investigator. She figured out where Sherlock was because a witness mentioned seeing chalk or powder on his shoes.
Also, the reveal that Holmes filled the brownstone with dozens of weapons.
"The Red Team":
For some people, seeing Holmes finally get called out by Gregson for acting like he's better than people because he's smarter than they are was definitely a moment of awesome, especially when he tried to smooth things over with a rather insincere apology. As part of that, Detective Gregson's punching him in the gut.
Holmes, finding out the killer's location by the radio frequency and taking him with a Singlestick, which is a skill straight from Doyle's canon. And since he didn't stick to the rules of where to hit in Singlestick, perhaps this is the beginning of Holmes' use of baritsu.
Watson: She gets evicted by her landlord because the person she was subletting to made a pornographic film in the apartment, she quickly discovers proof that the landlord was in on making the films. She uses this to blackmail him for money to put her things in storage and for a couch to replace the one that was violated in the film.
Joan telling Rhys if she even thinks he's a risk to Holmes' sobriety, she won't hesitate to turn him in to the cops.
Joan takes out an armed gunman by smashing Angus over his head.
Joan calling out Sherlock after he comments on her period.
Joan: Couching it as a scientific observation totally negates the misogyny.
And when a desperate Rhys tries to get Holmes to fall off the wagon in the belief it will help find Emily, Holmes attacks him, followed later by coolly calling off their friendship.
Watson looks in one of Bell's old files and quickly notices that Bell blew the whistle on a detective who planted evidence during a previous case. This turns out to be the crucial clue leading to the identity of the person looking to frame Bell. Note: This is a clue that Holmes, with all of his deductive skills and observational acuity, did not catch. In other words, Watson just solved the case, by herself, with nothing more than a passing glance at an old case file.
Watson getting back at Sherlock's misguided jump attacks on her by knocking down his wall of locks and then later beaning him in the face with a basketball (he had hit her in the back with a tennis ball).
Marcus Bell's brother Andre using his own blood to write that Bell didn't shoot him, figuring out immediately that his getting shot was part of the frame job. And he didn't actually see who did it, but knew it couldn't be Bell despite their tempestuous relationship.
"Deja Vu All Over Again":
Watson increases her awesomeness rating by solving her first solo case and the murder that Holmes was working on.
The villains get one with their utterly brilliant plan to steal millions of dollars without anyone knowing. Sherlock even says he'd be inclined to let them get away with it if they hadn't killed a man.
You have to give some points to the guard at the beginning of the episode: The fact that he managed to get a shot off at all was no small feat considering that he was bleeding to death, but it becomes a CMOA when you remember that he not only got a shot off, he sank a bullet into one of the thieves. This even led to Bell's CMOA above: If the guard had missed, the female thief would never have been caught.
Marcus Bell gets one when he goes to interview a brunette female hospital patient, notices a strand of blonde hair on her clothes, is able to determine then and there that the strand is from a blonde wig (implicating her in the robbery) and busts her all by himself.
In "A Landmark Story" when Moriarty realised that Daniel Gottlieb was captured she sent him a message which Holmes tries to have Gottlieb translate, but he can't. He shows it to Moran and it turns out to bean order to Moran to kill himself.
Watson figures out that Moriarty has fallen for Holmes as much as he's fallen for her and devises the trap that captures her.
The reveal of Moriarty is already cool, but it becomes even more awesome in retrospect. She played a completely different person from herself for two years, presumably while still running her network, utterly flawlessly, and was just gearing up for another long game when Sherlock noticed her missing birthmark. Her scheme in the episode is also damn clever, only failing because Sherlock and Joan were able to catch her at the literal last minute.
Watson holding her own during a meeting with Irene/Moriarty.
The opening minutes of the season premiere "Step Nine" have Sherlock solve a months-long case in a few minutes by following a bird, capped by Watson kicking the crook's ass with what's probably the same baton Sherlock used on Moran.
One for the villain of "Solve For X. She came up with a solution to P vs NP, a famously difficult Real Life math problem. Granted, since we don't actually see her solution, it's sort of an Offscreen Moment of Awesome, but we have to be fair to the writers here. They aren't mathematicians and, as no such proof has actually been formulated yet, they really had no choice but to just tell us that she solved it.
In "We Are Everyone" Joan finds a way to track down a suspect: she pickpockets his watch. Sherlock is both impressed and flabbergasted.
Sherlock and Mycroft have a singlestick duel in "Blood is Thicker". Sherlock wins.
Gregson gives a speech in "On The Line" pointing out that the job of the NYPD is to protect the citizens of New York and commends his officers for their good work in this regard. Then he mentions the complaints that have been made about him giving Holmes and Watson too much sway in investigations. He responds to these complaints by defending Holmes and Watson as helpful to the department and pointing out that if any of his officers have a problem with how he uses the resources at his disposal, then there's a conveniently located door they can use to show themselves out. Even better: This was meant for a rather stupid Jerk Ass detective who wrote off a Serial Killer as a suspect in his murders out of pure laziness, then told him where Joan and Sherlock live. "Screw you" has never been so grand.
"The Diabolical Kind":
Moriarty calmly executing her former associates who kidnapped her daughter, all while bleeding rather profusely from the wrists. She might be a villain, but she's a villain with some serious skills.
A hint of an ongoing one, for Holmes: he's made such an impression on Moriarty that the ruthless, sociopathic criminal mastermind goes out her way not to kill her FBI guard, even though it would have made her escape easier and faster because doing so would have disappointed Holmes.
An offscreen moment of brilliance for the government: how do you keep a genius and utterly amorally ruthless, yet beautiful and charming, female criminal who is known to be brilliant at seducing and manipulating people in custody? Make sure there's only one person who has contact with her. And he's gay. And said contact person is almost as smart as she is. After being told "Do you know I have sixteen escape plans?" He merely replies nonchalantly, "I only counted ten."
From "All in the Family": Holmes' "The Reason You Suck" Speech that convinces Bell (who is currently on bad terms with him) to investigate his boss in the Demographics Unit, whom Holmes and Watson (correctly) suspect of being corrupt, and ultimately return to what he does best—being a detective. "Be my friend, don't be my friend! Whatever. But don't be so foolish as to confuse punishing me with punishing yourself."
In "Ears to You", Lestrade gets his groove back with a little help or maybe not from Joan and Sherlock, and hunts down the guy who mugged him. His only regret is that it was too easy. Because of it being too easy, he becomes convinced that Sherlock conspired to help him in the case by pretending to be two witnesses that Lestrade interviewed. Sherlock confesses to this, then privately confides in Joan that he has never heard of either witness in his life. He was just telling Lestrade what he wanted to hear and Lestrade solved the mugging on his own.
It is a little shady, but after everything we've seen of Mycroft, which has mostly been underwhelming, he starts to really look cool in "Paint It Black". While working with Sherlock to find a man who stole a list of bank accounts in order to trade that man for Joan (who was captured by mobsters Mycroft is in bed with), Mycroft is seen talking to his mysterious employer. When Mycroft and Sherlock recover the list, Mycroft tazes Sherlock and takes the list. Then Mycroft shows up alone to get Joan back, giving the bad guys the list. Unfortunately, much as Sherlock warned him, they decide to kill Mycroft and Joan anyway. Mycroft asks if he can talk them out of it, they say no, so Mycroft asks for a few last words. They agree and Mycroft says "Paint it black." The mobsters are immediately taken out by MI6 snipers under Mycroft's command, a secret even from Sherlock. Mycroft was not pleading for his life but was actually trying to convince the mobsters to save their own lives by walking away and not forcing him to have them killed.
Despite his longstanding dislike for his brother, despite his anger at the various things he's discovered relating to Mycroft's work for MI6 and his certainty that Mycroft is breaking up Sherlock's relationship with Watson, in "Art in the Blood" Sherlock realizes immediately that his brother is being framed for murder and warns him.
In "The Great Experiment", Watson foils an attempt by Mycroft's handler, who framed him as the mole to threaten her into revealing Mycroft's location, by revealing that she is on a video call to Everyone. Even better for the fact that she had less than 30 seconds to come up with the plan.