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).
Suggested correction: It's because these episodes were aired out of order.
That's true because of Electric Soldier Porygon.
Pokemon, I Choose You! - S1-E1
Continuity mistake: When the capsule containing the three Poké Balls first opens up, you can see the names of the Pokémon etched into the balls (in Japanese), but when Ash picks them up, the names are gone.
Flower Power - S3-E6
Continuity mistake: When the person giving flyers says, "It's a giant outdoor Pokémon entertainment festival!" there is a man in the background with a blue shirt, but in the next shot, he has a yellow one. (00:01:58)
The Battling Eevee Brothers - S1-E38
Continuity mistake: When Pikachu and Eevee are first talking, the beam closest to the screen is smaller than the others, but in the next shot, it is larger. Also, there is a tree to the left of Pikachu, but in the next shot, there is not. Additionally, Pikachu is next to the plate of food while Eevee is one centimetre away from it, but in the next shot, he is two centimetres away from it while Eevee is three centimetres away. (00:09:48)
Island of the Giant Pokemon - S1-E17
Continuity mistake: When Jessie says, "Well, you can use a good workout," the window frame in front of her and James is black, but in the next shot, it is instantly cream. (00:13:31)
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.
Continuity mistake: In both "Attack of the Prehistoric Pokémon" and "Charizard Chills", Charizard carries Ash on his back without any trouble. However, later on in "Charizard's Burning Ambitions", Ash is suddenly too heavy for Charizard to carry.
Continuity mistake: In the early episodes of the Advanced Generation series, May is portrayed as being slightly taller than Ash. As the series moves on, May is consistently portrayed as being slightly shorter than him.
Continuity mistake: When Jessie says, "Guess we woke up this sleepy dump," she has lipstick on, but the next shot shows her immediately having no lipstick. (00:12:22)
Hiwada Town! Yadon's Well!! - S3-E26
Continuity mistake: When Misty says, "I bet it hasn't rained here in months," Brock is holding the map towards the bottom, but in the next shot, he holds it in the middle. (00:07:18)
Hinoarashi! Catch It!! - S3-E25
Continuity mistake: When Misty asks, "Ash?" the combination of the grass and dirt changes. (00:02:26)
Continuity mistake: When Ash is walking to the torchbearer, the people in the background change. (00:03:32)
Continuity mistake: When Ash first uses his Pokédex to learn facts on Snorlax, his right index finger is aligned with another one, but in the next shot, it is not. Also, his right ring finger is not aligned with another one, but in the next shot, it is. (00:07:40)
Big Panic! Kimawari Contest!! - S3-E19
Continuity mistake: When Ash says, "Water!" the puddle near the one under the leaking pipeline is more to the left of it, but in the next shot, it is more to the right of it. (00:01:40)
Continuity mistake: When Ash says, "Misty'll take good care of your Marill, you'll see," Wilhomena is holding her parasol with on hand, but in the next shot, she is holding it with two. (00:09:16)
Suggested correction: I rewatched the shots, and Wilhomena is holding her parasol with both hands in both of them.
Kikyo Gym! Sky Battle!! - S3-E15
Continuity mistake: When Pikachu agrees after Ash says, "Someday, I'll go back and see my old friend," his mouth is open, but in the next shot, it is closed. Also, Brock is to the left of Ash, but in the next shot, he is not. (00:06:32)
The Ninja Poke-Showdown - S1-E32
Continuity mistake: When Misty asks, "Brock, what kind of crazy place is this?" her bag is under and next to her, but in the next shot, it's not under her and is 0.33 metres away from her. (00:03:24)
Dai Pinch! Madatsubomi no tô - S3-E14
Continuity mistake: When Zacky is excited to meet Ash, Lizzie's mouth is open, but in the next shot, it is closed. (00:02:50)
Continuity mistake: When Ash and friends turn to look at Growlithe's mansion, Brock's left bag goes from brown to red. (00:02:31)
Continuity mistake: When Arielle lands on the bridge, she is on two planks, but in the next shot, she is on one. (00:03:49)