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.
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: 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)
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)
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)
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 Ash says, "Isn't it cute?" the strip on his left shoe to the left of the shoelaces there is white, but in the next shot, it is black. (00:04:12)
Battle Aboard the St. Anne - S1-E15
Continuity mistake: When James asks, "Are you addressing me?" the people behind him change. (00:08:52)
Continuity mistake: When Officer Jenny says, "It's here for the raising and protection of Pokémon," the map near her changes designs. (00:02:07)
The Path to the Pokemon League - S1-E8
Continuity mistake: When Ash is surprised by what he sees in A.J.'s Gym, the marks on his cheeks go from being present to being absent and then back to present. (00:08:17)
Here Comes the Squirtle Squad - S1-E12
Continuity mistake: When Officer Jenny says, "It's a real shame," Ash goes from having no part of Brock's left sleeve to the right part of Ash's right sleeve to having part of it. Also, he goes being in front of and to the side of Misty to being only to the side of her. (00:05:20)
Continuity mistake: When Ash is excited to see Ritchie when they are in the crowd next to the van, the people around Ash change. (00:06:41)
Continuity mistake: When the elevator doors open to the first floor, the part of the elevator indicating where it is has its background grey, but in the next shot, it is black. (00:05:31)
Continuity mistake: When Ash brings Pikachu to allow Ritchie to power the elevator, his right jacket strip goes from being absent to being present. (00:05:02)
Continuity mistake: When Brock mentions that Ash has to win on the rock, grass, water, and ice fields to compete at the Indigo Stadium, a staff member of the Pokémon League is not smiling, but in the next shot, she is. (00:03:07)
Abra and the Psychic Showdown - S1-E22
Continuity mistake: When Sabrina's father warns Ash about the Saffron City Gym, the buildings in the background change colour and design. (00:06:50)