Instead of being forced to flee like in canon, Team Rocket hides under their wooden shelter to avoid the Beedrills' stingers and even manage to capture the whole hive of twenty-one after exploiting their Logical Weakness to smoke. May also double as Fridge Brilliance when you consider that Koffing and Spearow defeated the hive, and they were the first ones of Team Rocket's Pokémon to evolve.
The same as in canon, once Ash realizes why he lost to Brock, he refuses to accept Misty's help (her Water Pokémon being strong against Brock's Rock/Ground-types). Both the sentiment and Ash's sheer determination are quite inspring.
"I'll win my first badge by myself with Pokémon I'm raising!"
Jessie's Hold the Line moment in Mt. Moon where she baits Ash and co. into a three on three battle. She can only half-direct her Pokémon, but does her job of stalling the trio long enough for James and Meowth to prepare their escape.
The way he does it counts too. When Staryu hides underwater, Ash has Pidgeotto vacuum him out with Gust to suck up the water. After noticing that Pidgeotto is tired, he switches out for Butterfree to buy time for him to rest, but still manages to win by having him use his newly learned Supersonic to confuse Goldeen before washing her out of the pool by making a wave with Whirlwind. Granted, he didn't actually know that water conducts sound, but he still could've pulled the same trick with Pidgeotto to win.
Despite thinking that he couldn't learn any more moves, during Meowth's training outside Cerulean City, he managed to learn Swift.
In a similar vein, Meowth demonstrated (albeit offscreen) his negotiation skills by 1) talking Giovanni into forwarding them some miniature Vacuum-Packs to help with the raid and 2) swinging a raise out of the deal for Jessie, James and him for bringing in such a large haul of rare Pokémon.
Ash pulling a Desperate Object Catch with his hat to catch a lit bomb and throw it into the sky in order to save the Pokémon of the hidden village.
Charmander manages to take on all of Team Rocket's Pokémon sans Koffing in order to keep them from getting away with Pikachu in Chapter 8.
Chapter 9 has quite a few for Team Rocket:
Instead of being obsessed with catching Pikachu like in canon, they recognize that a squad of wild Pokémon is a unique find and even think that they can be the first all-Pokémon squad on Team Rocket.
When the Squirtle Squad came into their camp to steal their food, not only did the trio not fall for their pitfall trap, but Jessie had Ekans attack from underground to separate the leader and hold him hostage.
From there, Meowth managed to (despite the leader's muffled protests) manipulate the four other Squirtles into willingly being captured to let their leader go. Team Rocket honors their agreement by having Mankey punt the leader as far as he can.
After Ash manages to escape the net, Team Rocket denies him any chance of rescuing the Squirtle Squad by activating rocket boosters on the hot air balloon. They get away with that and the help of Weezing's Smokescreen.
"If I'm such a lousy Trainer, why do I have the badge from your Gym?"
During the attack on the St. Anne, Team Rocket springs a legitimate ambush on the passengers, having Pokémon to counter their own as well as a massive cage with Artificial Limbs to grab enemy Pokémon. If the St. Anne hadn't sailed into a massive storm and forced Team Rocket into a Tactical Withdrawal, they could have very well robbed every Trainer on board, even Ash if they could've focused enough firepower on him.
Ash and Squirtle sliding onto the descending cage to free the Pokémon inside. With his rebreather, he's able to breathe underwater when the submarine submerges. Using Krabby, he forces the two pilots to flee under threat of the glass on the cockpit breaking.
By extension, Krabby evolving into Kingler to lift the abandoned cage to the surface.
James's newly bought Magikarp evolving into Gyarados to save him from drowning.
After which he One-Hit KO's both Beedrill and Weezing and then summons a giant tornado to send Team Rocket flying over the ocean.
James managing to talk down Jessie from Revenge Before Reason. It may not seem like much, but considering that it's Jessie, it took some guts to attempt. Actually doing it just makes it all the better.
James subduing each and every rejected recruit for Team Rocket with minimal effort. Culminates in taking out Damian with nothing more than Knockout Gas before turning him into the police for Pokémon abuse.
During Meowth and Cortez's battle, he refuses to give up, even when faced with next-to-impossible odds. A Rhydon that resists all of his ordinary attacks? Douse him by busting a water line! A Kangaskhan he has no chance of beating? Fight to your last bit of strength!
Jessie's battle against Cortez utilizes quite a bit of clever thinking and sheer guts on both her part and her Pokémon. When Golduck has Beedrill trapped, she demands to see Beedrill's eyes to let him decide if she should recall him, only to use the move to shoot poison in Golduck's eyes. After Beedrill poisons Machoke, she dawdles on sending out her next Pokémon until Cortez recalls it. Fearow manages a Defiant to the End against Kangaskhan and tells her she hopes the cut she gave her scars. Lastly, Ekans manages to break Kangaskhan's wrist then evolves to Arbok to defeat her.
Gastly: What's wrong with you?! What kind of human would put himself through that kind of pain?
Ash: I'd rather take the pain than be used against my Pokémon!
To help Team Rocket escape an enraged Gengar, Gyarados blasts it and Pokémon Tower with Hyper Beam.
As sad as the circumstances were, Butterfree activating his psychic powers and using them to unleash a No-Holds-Barred Beatdown on Team Rocket was nonetheless awesome.
Brock defeating Misty without losing any of his Pokémon. And he didn't rely only on Zubat (his only Pokémon that isn't weak to Water); all of his Pokémon get a win, showcasing the strategies he's been developing to combat Water-types.
In Chapter 28, Burton successfully defeats Sabrina and rescues Meowth.
Pikachu "accidentally" missing Kadabra with a Lightning Arrow, forcing Sabrina to release her Psychic Strangle on Ash.
After Team Rocket is blasted into a den of Primeape and suddenly weakened, Gyarados comes out of his ball and curls around them to protect the team. Then James shocks himself with the Zap Sapper and takes on a dozen Primeape, knocking out five and driving off the rest.
Ash manages to win against Erika in a three-on-three match with only two Pokémon and without using Pidgeot.
When attacked by a Fearow's Drill Peck with his Pokémon out of position, Ash catches it's attack long enough for Pikachu to Thunderbolt them both before Primeape performs a No-Holds-Barred Beatdown on Fearow for daring to attack his trainer/student.
Sabrina showing up to foil Proton's second attempt on Ash's life, just in time to save Brock from a falling platform.
Ash and Gary finally have their first battle. Not only Ash's Rattata manages to evolve mid battle, taking out Gary's Nidorino and Haunter on her own, but she even prompts Gary to evolve his Growlithe just to stand a fighting chance. Ash then brings out Charmeleon, who even after realizing he might lose decides to go down swinging and manages to injure Arcanine so badly that Gary decides to forfeit to save face, knowing Arcanine won't stand a chance against a fresh Pokémon.
Team Rocket planned their attack, knowing that Ash would side with the local Pokémon, and sent a separate team to capture him: Attila and Hun. Yet Ash's Pokémon still manage to beat them and send them packing.
Special mention to Kingler, who fools them into thinking he was attacking their Onix with the Hyper Beam, and he was actually aiming for Skarmory. And later, he cracks Onix's rock skin with his King Crabhammer.
Brock's Geodude evolves at the end of the battle. The higher stakes are paying off with his training.
Noah, from the Underground Tournament, is back, and he has not forgotten what James did to him. This time, using Johto Pokémon, he sent the Team Rocket member's whole team packing, even defeating his Gyarados.
Jessie is revealed to have once been a ninja under Koga's tutelage and she actually beat him in a fight by combining her ballet lessons with his fighting style. Koga even mentions how proud he was of her and he incorporated her fighting style into his own.
Koga's reveal that he incorporated Jessie's Dance Battler style into his teachings is one in itself, showing that he is not too proud to learn from his former students. It allows him to defeat her in their latest fight, even inflicting a paralyzing toxin on her. Despite this, Jessie still escapes.
Staryu freeing some kidnapped Voltorb all by himself and managing to evade Gyarados for some time.
Pidgeot making his canon counterpart look like a joke by defeating him in two moves.
Pikachu mastering Double Team to evade Charizard long enough to launch a Thunder attack that rendered him grievously injured.
Satoshi and his Pokémon also had their fair share of moments:
He figured out a way to stall Squirtle by using a Leech Seed net long enough to charge a Solar Beam. Unfortunately, Squirtle dove into the water and tunneled away from the blast with Dig, also allowing him to uppercut Bulbasaur for the knockout.
When Satoshi asks Muk if he has any long distance moves, he thinks about it for a moment before improvising a stretching punch that actually manages to connect with Charmander, who had been outmaneuvering him thanks to a difference in speed.
After Pidgeotto's crushing loss, Satoshi starts falling into a Heroic BSoD. But after some reassurance from Pikachu, he stands up again and decides to fight to the end.
Satoshi putting his foot down with Charizard, not once, but TWICE.
The first time, he says that while he won't give orders since Charizard won't listen anyway, he's also not going to recall him. This leaves him with two options: fight or let himself get beat up.
When Charizard refuses to give up the battle despite the fact that he can barely stand after taking Pikachu's Thunder, Satoshi stands between Pikachu and him as the former prepares to attack again and orders his Pokémon to stand down.
Satoshi:(To Pikachu) That's enough. Charizard's clearly in no condition to battle anymore. You win. (To Charizard) I'm still your Trainer. You may not care about that, but I do, and I'm not letting you get even more hurt. You can hit me in the face with a Flamethrower later. Return.