The "fighting is wrong" moral ending exists only in the American version. In the original Japanese, the ending was that Mewtwo accepted it could be a proper Pokemen in spite of having been brought to life by humans, because Ash (Satoshi in the original Japanese) is still a proper human in spite of just having been brought (back) to life by the other pokemon. See more...
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Other: 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).
Character mistake: When Meowth is naming the different types of Pokémon being cloned (while Ash and the other trainers are running around upstairs), Meowth calls one of the Pokémon "Sandshrew." The Pokémon is in fact Sandslash, Sandshrew's evolved form. This is a character mistake arising from Meowth's ignorance of other Pokemon species (not that he's been shown to be ignorant, but in this solitary case, he is).
Other: 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.