Pokemon (1998)

So Near, Yet So Farfetch'd - S1-E47

Continuity mistake: When Team Rocket takes off in the boat, it sinks. Their pokeballs float away, and Jessie says "Arbok and Lickitung are floating away!" But she doesn't catch Lickitung until Princess versus Princess (Season 1, Episode 52).

Dig Those Diglett - S1-E31

Character mistake: Brock states that the Diglett are plowing the ground and the Dugtrio are planting the trees, but the opposite is true (The Dugtrio are plowing, and the Diglett are planting).

The Ninja Poke-Showdown - S1-E32

Factual error: When Venonat uses Stun Spore, Ash tells Bulbasaur to use Whirlwind. Bulbasaur just blows the powder away with his mouth, but he doesn't use the Whirlwind attack. He can't learn Whirlwind in any of the games, and what Whirlwind is supposed to do is to blow the opposing Pokemon away. Ash could have just as easily told Bulbasaur to blow it away, but he instead chose to tell him to use a move that he can't possibly learn. The only Pokemon that can learn Whirlwind are either Flying types or Bug types; i.e., Pokemon with wings (with the exception of Makuhita and Hariyama, which weren't introduced until generation III, and did not exist at the time this episode aired). In The School of Hard Knocks (Season 1, Episode 9), a character mentions information regarding a Pokemon's levels, attacks, and information which is taken straight out of the game, so it's very clear that Bulbasaur should not be able to use Whirlwind.

Pokemon, I Choose You! - S1-E1

Continuity mistake: When the capsule containing the three pokeballs first opens up, you can see the names of the Pokemon etched into the balls (in Japanese). But when Ash picks them up, the names are gone.

Round One: Begin! - S1-E75

Character mistake: When Mandy brings out Golbat, Brock says "Kingler is really weak to air attacks." But Kingler's a Water type, which has no weakness to Flying type attacks.

A Chansey Operation - S1-E45

Factual error: When we see that Dodrio's neck is tangled, the configuration doesn't make sense. It just looks like two bands of neck, but it doesn't reflect what it would actually look like if it was really tangled.

The March of the Exeggutor Squad - S1-E41

Other mistake: The Pokemon Exeggcute is shown evolving in to an Exeggutor naturally. But the Pokemon Exeggcute can only evolve into an Exeggutor with the use of a leaf stone.

Volcanic Panic - S1-E57

Character mistake: During the recap, the narrator says that Ninetales had defeated Squirtle by using Ember, but Blaine ordered it to use Fire Spin.

Bulbasaur and the Hidden Village - S1-E10

Other mistake: In the scene when Team Rocket tries to steal the Pokemon, Bulbasaur saves Oddish. Ash comes to help push Bulbasaur, and for a few frames you can see 2 sets of hand prints cut out where Ash's hands go.

A Chansey Operation - S1-E45

Continuity mistake: Jessie seems completely surprised when she's told that Voltorb can explode, but in The Ninja-Pokemon Showdown (Season 1, Episode 32), not only did she and the others find out what Voltorb are, they were all affected by the explosions as well.

Round One: Begin! - S1-E75

Factual error: Krabby evolves into Kingler during the match, and is somehow able to use Hyper Beam. Krabby can't learn Hyper Beam, and Kingler can only learn it via a Technical Machine.

Round One: Begin! - S1-E75

Character mistake: When Team Rocket first sees Mandy doing his magic tricks, he produces a bunch of Pidgey. Meowth says "I like those Pidgeotto." He's dealt with Ash's Pidgeotto on numerous occasions, so there's no reason that he shouldn't be able to tell the difference.

The Pi-Kahuna - S1-E67

Revealing mistake: When Pikachu meets Puka on the cliff, we are treated to an aerial shot which shows the ocean below. There is sunlight reflecting off the surface, but as the camera moves, the lights pass in front of the two Pikachu on the cliff.