Plot hole: Spiro's vault can only be opened by Spiro himself, but the guards change every hour and Spiro doesn't go to the vault every hour of his life to let the guards in, so how do they get in?
Continuity mistake: In the second book it says that Artemis' father's last memory was waving goodbye to his family but in one of the diary extracts, when Artemis is at the hospital with his father, his father talks about his time as a prisoner, which he shouldn't be able to remember.
Continuity mistake: In Chapter 10, Fingers and Thumbs, Spiro tells Artemis that his cousin Costa had surgery so that he could take his place. Spiro had set the gel scanner to accept Costa's fingerprint for one night only. Later in the chapter Artemis claims to have reverted the cube from version 1.2 to 1.0. After Spiro tests the cube he claims "I have no family, no heirs." This statement contradicts what he had said about his cousin. He could not possibly have a cousin and no family.
Plot hole: The cube is suppose to be a tiny box, but Artemis retracts a keyboard from it at the end of the book. Surely that would be too small for your fingers to press the keys?