Challenge of the Samurai - S1-E4
Continuity mistake: When Ash goes to get a Poké Ball for the first time, the ball is upside down, but in the next shot, it is upright. Also, behind the same Poké Ball, there is another one, but in the next shot, there is not. (00:03:19)
Continuity mistake: When Lily says, "The water show," her right hand is outstretched, but in the next shot, it is by her right side. (00:03:58)
Bulbasaur and the Hidden Village - S1-E10
Continuity mistake: When the camera begins panning up to Ash and Brock tending to a Staryu, a saucepan appears from nowhere. (00:10:28)
Continuity mistake: When Professor Oak and Delia are first seen watching Ash's first battle at the Indigo Plateau Conference, Delia has a person to the left of her, and her hands are in her lap, but in the next shot, she does not have a person to the left of her, and her hands are clasped together. Also, she and Professor Oak are smiling, but in the next shot, they are not. (00:11:46)
The Path to the Pokemon League - S1-E8
Revealing mistake: When A.J. and his Sandshrew walk into a tent, A.J. and his whip clip through the tent. (00:07:56)
Electric Shock Showdown - S1-E14
Continuity mistake: When Ash picks up the Thunder Stone, his belt buckle is brown and black, but in the next shot, it is instantly grey and black. (00:11:13)
Continuity mistake: When Oswald begins testing the joystick, there is a button that is green, but in the next shot, it is blue. (00:16:10)
Charmander: The Stray Pokemon - S1-E11
Continuity mistake: When Brock stands up from the stool he is sitting on, his left hand is on the table, but in the next shot, it is not. (00:07:01)
Continuity mistake: When the doors to the Pokémon Center are opening, a frame changes from grey to white between shots. (00:05:09)
Revealing mistake: When Ash brings his first piece of meat into his mouth, another one disappears into thin air. (00:09:09)
Abra and the Psychic Showdown - S1-E22
Continuity mistake: When Ash notices the Saffron City Gym, the buildings in the background change. (00:06:38)
Other mistake: When Ash, Misty, and Brock are worried about the cyclone approaching, the edges of Meowth's ears are mistakenly colored tan instead of black. (00:20:08)
Island of the Giant Pokemon - S1-E17
Other mistake: In the recap, when Ash, Misty, and Brock are worried about the cyclone approaching, the edges of Meowth's ears are mistakenly colored tan instead of black. (00:01:16)
Character mistake: When first showing the tournament from the front, a sign misspells Pokémon Number One as "Pokemon Number One." (00:07:46)
Pokemon, I Choose You! - S1-E1
Continuity mistake: When Gary is first talking to his crowd, there is a woman with blue-green hair, a pink dress, and a yellow apron to the left, but in the next shot, she is replaced by a boy in a green shirt with brown hair and without an apron. (00:05:11)
The Fourth Round Rumble - S1-E77
Character mistake: When a poster for the Pokémon League is seen, it misspells it as "Pokemon League." (00:20:22)
Mystery at the Lighthouse - S1-E13
Other mistake: When Brock turns his head to the costume, his nose is missing. (00:12:47)
Suggested correction: Agree with the other correction. Dropping details, such as facial features like a nose or mouth, and simplifying character designs is a very common and encouraged drawing/animation technique to imply distance. This isn't something the animators would just overlook. It was a deliberate decision. Ash and Misty similarly look somewhat less detailed than they do in closer shots. At best, this would be a deliberate mistake, but I personally think it falls under the umbrella of "suspension of disbelief" and shouldn't be considered a mistake given it's a stylistic choice to imply distance.
Suggested correction: His nose isn't seen because he is far away from the camera.
Continuity mistake: When Brock says, "Looks like a greenhouse," he is holding the straps of his rucksack, but in the next shot, he is not. (00:04:08)
Tentacool and Tentacruel - S1-E19
Revealing mistake: When Brock says, "Ah! Zubat!" his neck is not fully colored in. (00:15:50)
Who Gets to Keep Togepi? - S1-E48
Character mistake: At the beginning of the episode, the sign on the Pokémon Center misspells Pokémon Center as "Pokemon Center." (00:01:13)