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).
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. [This is a result of mistranslation. In the original, Japanese version Ash orders Bulbasaur to "blow it away." He didn't say Whirlwind. Still a mistake in the English version.]
Plot hole: Officer Jenny asks Ash what he knows about the "trio" when he tells her that the pirates are likely Team Rocket, but he hadn't said anything about there being three of them before that. And Jenny obviously didn't know anything about Team Rocket, either. (00:05:30)
Character mistake: Ash's Chikorita is knocked out by Bugsy's Metapod in the Gym battle against him. Brock mentions that Ash's remaining Pokémon are Cyndaquil and Pikachu, and Ash says, "I'll save Chikorita for later and use Pikachu now." However, Chikorita is the Pokémon that was just defeated, and Ash's remaining Pokémon is actually Cyndaquil, as mentioned by Brock. (00:11:20)
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. In the Japanese version, there is a mention that something in these woods causes Exeggcute to evolve without using the Leaf Stone (when Exeggcute evolves, James even mentions that there is no stone). However, as this was skipped in the English version, it creates a plot hole.
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)
Plot hole: After Ritchie tells Misty that he never talked to them through a phone, Misty could have put two and two together and realised that Ash was told to go somewhere by someone impersonating Ritchie and that he might be in serious danger. However, she does absolutely nothing to help Ash, she doesn't even inform Brock about it.