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. [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.]
Dark Specter's Revenge: Part 1 - S1-E29
Factual error: Bulk, Skull, and the Professor try to get in a Apollo Saturn V rocket to escape Earth. They head up the tower, and are seen getting into the ship via the thin pillar at the top - this pillar was used in case there was an emergency early on in the launch. Astronauts got into the ship in the Command Module, which was slightly lower down.