Continuity mistake: When Ash & co. are in the boat with Team Rocket (who's dressed as Vikings), watch Brock's shirt sleeve (The one away from Misty) when Misty puts Togepi inside her knapsack. It goes from a dark orange to green (the same color as Brock's vest) for a few frames before turning back.
Other mistake: When the Poké Balls containing the Trainers' various Pokémon are sent to the DNA Cloning machine, Team Rocket incorrectly identifies Scyther as Alakazam. This is a dubbing error as, in the original Japanese version, the Rocket-dan (as they are called) correctly identify the Pokémon as a Strike (Scyther's Japanese name).
Other mistake: Meowth calls one particular Pokémon in the test tube-thing a Sandshrew, however it is a Sandslash. This is a dubbing error, as Nyasu (Meowth's Japanese name) correctly identifies the Pokémon as a Sandopan (Sandslash's Japanese name) in the original Japanese version.
Continuity mistake: When Brock looks at the picture of Nurse Joy, in the closeup of the picture Brock casts a shadow on it, but in the previous shot he didn't.
Character mistake: One of the other trainers said he rode over on a Pidgeotto, but it was a Pidgeot.
Continuity mistake: When Fergus goes to Gyarados after Mewtwo reflects its Hyper Beam, you can see the back of a Nidoking, but Fergus has a Nidoqueen.
Audio problem: When Ash receives the letter from Dragonite, we hear Togepi say "Togepi?" but it's mouth doesn't move.
Other mistake: In Mewtwo Strikes Back, when the pirate trainer sends out Machamp (the four-armed Pokémon), the animation of it appearing is shown twice. Also, the sound effect that plays when a Pokémon appears isn't played the second time. There was a small section cut out of Ash throwing Squirtle's Poké Ball in the air. That was replaced with Machamp coming out twice.