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Artemis Fowl - 3 mistakes
Plot hole: When the time stop is almost over, Root uses his "finger" to render Cudgeon unconscious. However, later in the book it is explained that if you lose your consciousness during the time stop you would immediately jump to the end. Cudgeon should have disappeared, and Foaly (or someone else) should have realized how Artemis planned to escape.
Continuity: This is seen over two books; Artemis Fowl and Artemis Fowl: The Eternity Code. In Artemis Fowl, chapter two, Artemis cracked his knuckles when he was trying to decode the fairy Book. However in the eternity code, chapter 1, when Jon Spiro cracked his knuckles and it is stated that Artemis detests that habit.