From Bulbapedia, the community-driven Pokémon encyclopedia.
In the Pokémon manga, a situation will sometimes occur in which a Pokémon 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).
List of manga Pokémon with moves that they cannot learn in the games
Pokémon in How I Became a Pokémon Card will often use moves that they cannot learn in the games. However, this is because this series is based on the Pokémon Trading Card Game, so the "illegal" moves Pokémon use in this series are moves from their TCG cards.
Similar examples that are not manga move errors
Pokémon which can know the move in a previous game