Mikey's reasoning for why he should be the leader instead of any of his brothers? Well, he doesn't actually have a reason, he just thinks it'd be neat.
Mikey's face when he takes his first bite of pizza. And his brain subsequently exploding from flavor.
That scene in general, really.
Donny: Should we open it?
Leo: Careful! It may be dangerous.
While waiting for the kidnappers, Mikey and Donny start playing word games.
Mikey: Okay. I'm thinking of something green. Greeen. Greeeeen.
Donny: (Boredly) Is it Raphael again?
Mikey: MAN, You're good at this!
Donnie facepalming, forgetting he's wearing wall-climbing spikes on his hands.
After getting a mini-lecture from Splinter about how there are no "right or wrong" decisions, only choices, Leonardo learns he was chosen as the leader was because he asked for it. Shocked, he asks if Mikey would've been an option.
In response to Donatello geeking out over April and the fact her dad is a scientist in the second episode:
Donnie: This is awesome! That girl's dad is a scientist! I'm a scientist! Oh, she is so gonna like me!
Snake: ...I don't think you're her type.
Leo explains the stakeout:
Leo: For the last time: That building has the same logo as the van that took the family, so if we wait here long enough one of the kidnappers will eventually show his face and when he does we'll make him tell us where they took them.
Raph: No, you have to come up with a better plan, 'cause the four of us standing here with our thumbs up our noses-
Mikey: (looking at his thumbs) I don't think they fit...
April tries to escape the Kraang by faking sickness and attacking a Kraang guard. He doesn't even react when she grabs him or even when she bites him. Then he picks her off his back with one hand, puts her down, and locks her back in the cell with her dad.
And again when Baxter tries to come up with a name for himself. One particularly funny name he makes up that is just so absurd is "Captain Punch-You-Hard". Another, which Michelangelo admits he likes, was "The Suitinator".
As the Turtles are about to start fighting Stockman, Mikey screaming "WAIT!" & the subsequent shot of the other Turtles & Stockman frozen mid-battle, all looking at Mikey... Who just wanted to put the T-Pod away before he started fighting.
The intro itself gives Splinter a good moment.
Splinter: How many times have I told you not to skateboard in the lair?
Mikey:[Exchanges a look with Don] ...none, Sensei.
Don spying on April using Metalhead and talking about how she won't notice... and he forgot to turn off the speakers so April hears him, he then tries to cover it up and ends up hitting the megaphone button and embarasses himself even further.
The Shredder learning from Bradford what happened and how he failed his mission:
The Shredder: ...They defeated you with go karts and a water balloon?
Made even funnier when you realise that the Shredder is more confused than angry.
"Doctor Prankenstein". Especially when he gets Leo.
Raph: I can't believe I'm saying this but, 'get it together, Captain! You're our leader, so act like one!'
Leo: That was the anxiety ray talking.
Raph: What, that's it? You're not gonna slap yourself?
Mikey's explanation of where he got the pizza at the end. Double Points for him calling them out on their disgust, as pizza from a dumpster still in it's box is likely more sanitary than the worms and algae they've been eating before they came up top.
Michelangelo tries to offer a pizza milkshake, leading to this exchange:
Donatello: There's no way that can sound any less appetizing!
Michelangelo: I call it the "Pi-Shake"(pronounced "pee shake")
Donatello: (nearly vomits) I stand corrected.
On Leonardo's television show, the episode deals with these adorable pink fluffballs the crew has on their ship. The captain disposes of them humanely by ordering the airlock to open, and the aliens are sucked out while he sits there in his chair with a stoic look on his face, and smiles.
Raphael: You have to be the only one who likes this show.
Upon arriving in Leatherhead's booby-trapped hideout via a long underwater swim, Raph gets this gem:
Raphael: Whew! Sometimes, it's good to be a turtle.
(A stop sign comes from nowhere, slicing through the air between Don and Leo with Audible Sharpness. Raph ducks into his shell just in time to avoid being beheaded.)
Raphael: ...and sometimes, it's good to be a short turtle.
Near the end of the episode, we have this conversation:
Splinter: Leonardo, you are not the first man, or turtle, to make a fool of yourself over a girl.
Mikey: What about Donnie? *gets smacked*
Another from Splinter after he says he understands why Leo didn't tell them about Karai.
Leo: I was worried you'd be mad.
Splinter: Who says I'm not mad? (smacks Leo with his stick)
Bradford laughing at the malfunctioning robot legs that Stockman built for Xever.
"Fix this, or I'll bite your face off." (gets kicked in the face)
When Raph asks Leo if he's going to tell their brothers and Splinter about Karai, we have this little exchange:
Leo: No need, we had a little chat and she agreed to leave us alone.
Raph: Right, because villains always back off when you ask them to. Maybe I'll text the Kraang and ask them to stop mutating stuff.
Mikey can't come up with a fitting name for the large mutant they have to fight. He decides to just go with Justin.
Mikey screaming like a girl (as in a stock girly scream) when the DNA fusion is in the process of creating Justin. The funniest part is that, after showing tanks of armadillo, octopus, jellyfish, and electric eel DNA, Mikey screams at the tank of cat DNA.
Leo: Let's put old mother Hubbard back in her cupboard.
Leo, Raph, and Mikey are arguing about who gets to drive the Shellraiser and Don hits all 3 of them with his bo staff, assigns Leo as the driver, and when Mikey and Raph ask why, Don points out that Leo's the only one who won't use the Shellraiser to hit something for fun.
Leo imitating the Kraang along with April and Splinter's reaction.
Leo: "The ones who are working for this place must punch the card known as the time card into the clock known as the clock of time."
Donnie once again getting the face shaking treatment from Leatherhead.
A Kraang picks up Mikey's nunchucks, twirls them, looks happy, hits itself, and tosses them.
Don is trying to figure out where he's seen the Kraang's insignia before and Mikey repeatedly speculates it's the Olympics. Frustrated, Don yells at the others to leave him alone so he can solve this mystery, which was enough to scare even Raph and they back away. Splinter then walks up and also thinks it might be the Olympics.
And when Donnie yells at them, Mikey leaps into Raph's arms in the background.
Kraang 1: "I suppose Kraang has once again been foiled by the Turtles and failed to retrieve that which Kraang wants to retrieve."
Kraang 2: "Kraang is wrong. Kraang has retrieved the power cell. In Kraang's face!"
April: "This just doesn't make sense. If the Kraang want to terraform the Earth, why do they need my dad?"
Leo: "Well, he is a scientist."
April: "Yeah, but he's a psychologist. He studies rats going through mazes. (To Splinter) No offense."
When Stockman is asked why he became a villain, Stockman starts talking about his past hardships and at one point states he built a volcano for a science fair and used actual molten lava which burned down the gym and got him expelled.
Also, when Stockman describes himself as a sensitive, misunderstood child, Dogpound replies with a deadpan 'Well, there's a surprise.'
April's attempts at finding the right ninja weapon.
Splinter: You already possess the Kunoichi's greatest weapon. The mind.
April: Yeah, but when was the last time you saw someone hit a bad guy over the head with their mind?
The Turtles and The Foot Clan attack the Kraang at the exact same time. The baffled reactions of The Foot Clan sell it as well as Raphael being told to be pinched to see if he's dreaming. Mikey obliges, and gets hit for it.
The end of the episode. Wiped out from beating Stockman and his labyrinth, the turtles and Dogpound and Fishface try to start fighting again. Only to say screw it and go home.
Raph berates Leo for bringing Karai into the Shellraiser since she'll see all their technology. Karai sarcastically responds that they're doomed when Shredder finds out they have an ice cream cone-shaped lamp.
Mikey acts like the punching dummy is sentient.
Mikey: *responding to Raph hitting it* You're pretty tough when they can't fight back.
Mikey: *to the dummy when Raph knocks it on the ground* You'll get him next time.
Donnie finally getting to tease someone else for their crush.
Leo: If Karai can pull it off.
Donnie: Why, you worried about your girlfriend? I see why you guys do that, it's kinda fun!
The turtles training session using each other's weapons. Leo trips himself with Don's bo staff, Raph hits himself with Mikey's nunchucks, Mikey throws Leo's swords in the air and nearly cuts off his feet, and Don pokes himself in the chin with Raph's sais.