In the second episode of season 2—Diana's blase acceptance of her boss's request to pose as a call girl, and the culmination of her conversation with the thug sent to hurt her.
Diana: Draw, and I'll put a bullet through your shoulder. (His hand creeps towards his gun. She's faster, and she does exactly what she said she was going to do.) Diana: Told ya. (Her FBI buddies burst in to save her, and she gives them a big affectionate grin, her stiletto on the chest of the bad guy and her gun still trained on him.) Diana: Awww... You were worried.
In the ending of 2x03, "Copycat Caffrey", Peter addresses a criminology class, some of whose members are being been arrested for following in Neal's footsteps even as he speaks, in the style of an FBI recruiter, and telling 'em crime doesn't pay. He uses Neal as an example.
"I wear a badge. He wears a tracking anklet. Applications are on the table. (walks off)"
In 2x04, "By the Book", Mozzie cooks up a plan to get his romantic rival out of the way and save the girl, all within minutes. Then he—yes, Mozzie—disarms a criminal. (If you look closely, his trigger discipline is justterrible) Then he asks if he's going to become a consultant like Neal, showing he's made some significant headway in his issues with authority.
During this same scene, we can't forget Peter moving in alone and putting his gun on Navarro. To sum up, Navarro is not afraid to kill Peter, and he's being backed up by at least four men. Sure, Peter had FBI coming in moments after him, but going in alone and staring 5+ men down on your own is badass. Mozzie doesn't count as backup, since he was more or less keeping one unarmed thug out of the fight.
Peter chasing down and arresting Larson in the middle of Central Park on a freakin' HORSE! in "Burke's Seven".
And considering the bystanders pointing their phone-cams at him, you just know the whole shebang would show up on Youtube a couple minutes later.
When Diana arrives to arrest a criminal in "Countermeasures", he laughs her off and keeps walking away because he doesn't take her seriously. One Gilligan Cut later, we see Diana slamming his face into a car hood and delivering a delicious Ironic Echo.
In "Payback" Peter gets kidnapped, complete with the bag over his head to keep him from knowing their destination. Then, upon being un-bagged in a makeshift cell, he tells the kidnapper almost exactly where they are (within about a block).
Without moving from this cell, he then figures out the mastermind's plan, manages to convey it to Neal, and lures his jailer close enough that Peter can knock him out.
In the mid-season finale of season 2, Neal goes after Fowler, the man who he thinks killed Kate. They end up at a gallery showing artifacts which will soon be shipped to Russia. Peter has trapped Fowler inside a room, and while Fowler is trying to make a rope out of a sheet to escape, Neal sees him through a window. What does Neal do? He runs to a balcony on the second floor, grabs a cutlass, cuts the rope which has anchored a tapestry to the balcony, and jumps. We get an awesome slow-motion shot of Neal swinging on the tapestry and crashing through the window, then he takes the gun he stole from an antique shop and fires a shot that barely misses Fowler. All this while "How You Like Me Now" plays. Holy CRAP.
In "On Guard", though they may not have gotten away with it completely yet, Mozzie finally finishes his long con against Adler.
In 3x10, "Countdown," Neal in the sequence when he gets the Degas back from Richmond the arms dealer. After Briar Patching his way into a locked supply clsoet, Neal breaks into the penthouse, swaps the real Degas with the fake he made that Mozzie smuggled in via bazooka, replaces the fake in its hiding place. Then in the last moment before Richmond, Diana and Peter enter the scene, Neal exits the penthouse and jumps off the skyscraper with the Degas, using a parachute to stop himself from going splat. He then calmly walks away, detaching the parachute with ease, and gets back into the closet, where Peter finds him exactly where he left Neal; "What took you so long?"
And to make matters even better, Neal's fake is almost good enough to fool Peter's mentor, and he comments that if the forger had been just a little better, he would have missed it as a fake. Then the Fridge Brilliance kicks in and you realize that Neal purposefully wanted it identified as a good forgery, but still fake. He probably could have made a near-flawless copy if he had wanted to, since the "mistake" seemed to have been not aging the paper long enough in an oven, something Neal is smart enough not to have missed.
Whenever Neal puts his not-inconsiderable charisma and quick thinking to work. For example: in the above episode, Neal handles Agent Matthews showing up by formulating and executing a plan in a thirty-second elevator ride that simultaneously gets her to call him by his real name instead of the name he gave her and keeps her from mentioning she's met him before, both without raising her suspicions.
In "Checkmate": Elizabeth Freakin' Burke sending coded messages in front of her captor (seconds after he specifically told her not to)? Check. Scaring the pants off her other captor with a few words and a thermostat? Check. Using her jewelry to escape? Check, check and check.
And let's not forget Peter's Big Damn Heroes moment, tackling Keller as he's about to kill Neal. Of course, Keller threatens Elizabeth, but Peter tells him that she's safe and he has no leverage against him anymore. Having spent the whole episode at the the mercy of Smug Snake Matthew Keller, it was extremely satisfying to see Peter gain the upper hand.
One for the bad guys: Matthew Keller deserves some credit for his scheme in Season 1's "Bottlenecked": He challenges Neal to their old competition of recreating a forgery of a rare wine bottle. Neal goes along, seeing this as an opportunity to bust Keller for fraud. (There's one chemical test that no forgery can beat, no matter how good it is. The idea is that if Neal makes a good enough forgery, then both his and Keller's will have to be administered the test.) They are and Keller's passes. He had the real thing the entire time. All the intrigue associated with a forgery surfacing drove up the bottle's price at auction and Keller was able to sell it for seven figures. Neal wins in the end of course, but it's not every day that someone successfully puts one over on him like that.
Neal gets a very understated awesome moment in Brass Tacks, and it takes a little Fridge Brilliance to see it. After Peter is injured in a wreck because Pratt had the brakes tampered with on his car, a very upset Elizabeth says that she doesn't want the next call she gets about Peter to be from the morgue, so she insists that Neal do whatever it takes to keep him out of the loop on the search for what the key unlocks—even it means lying to him about it. At one point, she basically asks Neal if he knows what it feels like to find out that someone he cares about has been badly hurt. Hmmm...okay, let's see...
Out of the Box: Neal sees his girlfriend get blown up.
Point Blank: Neal's best friend is shot (and barely survives).
Parting Shots: The woman who pretty much raised Neal is shot (and doesn't survive).
Heck yeah, he knows what it feels like! And he had every right to get angry and point that out to Elizabeth. But he didn't. Instead, he agreed to do what she asked, even though it meant lying to the one person he never lies to.
In The Original, Neal is trying to explain how he knows that a piece of art in a museum is actually a forgery. The curator is standing there, going on about how the piece has already been authenticated, so it must be the real thing. Neal suddenly turns to her and asks if she's familiar with the process of chicken sexing (the look on Peter's face is priceless—he's just as confused as the curator!). Neal proceeds to give a detailed explanation about how baby chicks are sorted by gender, then just when it seems as though he's gone completely off the rails, he ties it back to the discussion about forgeries by explaining that there is a scientific basis for instinct, and no matter how convincing the piece of art may look, he just knows it's a forgery. He ends up being right.
The Mozart sequence near the end of Out of the Frying Pan. Somehow it manages to make pushing elevator buttons and pushing out a baby look like part of the dance. It's an incredibly choreographed scene.
Neal himself is simply a walking talking forever ongoing Crowning Moment Of Awesome. He's on a tracking anklet with a Properly Paranoid and extremely competent FBI handler and yet he still manages to pull off incredible heists right under their noses. Sometimes when he's surrounded by FBI agents and in a building staked out by FBI agents. He doesn't always get away with it since Peter is well, Peter, but he does about 75% of the time.
Neal can create a credible looking ID pass with nothing more than a magazine, a brochure, a pen knife and some glue. And he apparently carries around passport sized photos of himself, just in case.