In the Pokémon anime, there will often come up a Pokémon that knows a move it cannot learn legally in any of the games. It is unknown whether these are actual mistakes, a writing policy of not having to stick to the games too closely, or merely the Pokémon using an attribute that shares the name of a move in the games.
Occasionally, in-game event Pokémon that can be transferred onto the main series games have a move that is not normally included in that Pokémon's moveset (a prime example being Pokémon Box Ruby & Sapphire, which gave away four separate Pokémon with moves that were not normally available to that specific Pokémon).
Roxanne commands her Nosepass to use Hyper Beam, which it cannot learn. These errors were picked up on in the dub, and the references to Hyper Beam were replaced with Thunder Wave and Zap Cannon. However, there is evidence that there was an error in the original script, and it was meant to be an Electric attack. This is seen in Pikachu being able to absorb "Hyper Beam" as if it were an Electric attack, and it had physical similarities to Electric attacks.
While demanding Ash's Pikachu fight him, Pikachutwo repeatedly slaps Pikachu's face, while alternating from his right hand to his left. This savage barrage of physical strikes resembles DoubleSlap, a move which, although Ash's Pikachu does not know, Pikachu can legitimately know through breeding from Generation II onwards.
Multiple Tentacool are seen using an unidentified red beam attack. Tentacool's Pokédex entries state that it absorbs sunlight and converts it into beam energy, similar to SolarBeam. However, not only does this attack bear no resemblance to SolarBeam, Tentacool has never been able to learn this move. In fact, the only Beam moves Tentacool can learn are BubbleBeam, Ice Beam and Aurora Beam*, none of which resemble this attack.
When Ash has his Charmander use Leer against a Haunter, it appears to use the same move back at Charmander. However, Haunter has not been able to learn Leer in any Generation. It is possible that Haunter was simply countering Charmander's Leer.
Ash has Bulbasaur "lick" Psyduck's head and use its "tickle attack" with its vines. This is not to be confused with the actual moves Lick and Tickle, the latter of which was introduced in Generation III. Bulbasaur cannot learn either move.
Tony bites down on Jessie's Arbok, who is constricting it. However, Ralph does not order an attack, he simply uses its sharp teeth to free himself and Maria from Arbok's grip. This move resembles Bite but Nidoran♂ cannot learn this move.
Pikachu and TRMeowth ([[{{{2}}} (move)|{{{2}}}]]) fight against a giant Rhydon. When Meowth jumps on Rhydon's back, he states that he should try a Tickle attack. However, Meowth cannot learn Tickle in any generation yet, and Tickle was not introduced until Generation III.
Lugia uses an unidentified Psychic-type attack to break free of ice. The only Psychic-type attacks Lugia could learn when it eventually appeared in Gold and Silver are Dream Eater and Future Sight, which this move is unlikely to be, and Psychic, though the anime version of Psychic usually involves controlling an opponent. It is possible that Lugia is using Recover, a move Lugia can learn, and instead smashing the ice physically.
Entei hypnotises Delia in Spell of the Unown. However, Entei is unable to learn Hypnosis. This could be due to the fact that this Entei was merely an illusion, not a real Pokémon.
After living for 150 years, Ninetales found that it was able to use mysterious powers. One of these was the ability to lift objects with its mind, similar to Psychic
A wild Nuzleaf blew on a leaf to make Ash and his friends' Pokémon drowsy, though Nuzleaf cannot learn GrassWhistle. However, some of Nuzleaf's Pokédex entries do state that it uses the leaf on its head as a flute.
A Lunatone is seen using the moonlight to restore itself, though it cannot learn Moonlight. However, Lunatone's Pokédex entries do state that it gains its power from the moon.
Some Drifloon were used to fly around the area. The Pokédex states that a Drifloon cannot carry the weight of children. However, three are used at any given time. Similarly, it is also possible for Drifloon to carry players across short distances in Pokémon Ranger: Shadows of Almia.