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.
Plot hole: Artemis, Butler, and Juliet escape from the time stopped manor when they go to sleep. Artemis claims they escape the time stop by a change in consciousness. But earlier in the story, Butler and Holly get knocked out cold and don't disappear from the time stopped manor.
Continuity mistake: This is seen over two books: Artemis Fowl and Artemis Fowl: The Eternity Code. In Artemis Fowl, Chapter 2, Artemis cracked his knuckles when he was trying to decode the fairy Book. However, in Artemis Fowl: The Eternity Code, Chapter 1, Jon Spiro cracked his knuckles, and it is stated that Artemis detests that habit.