Continuity: When Dumbledore arranges his first lesson with Harry, he asks Snape to postpone Harry's detention for a week. Since Snape never specified a time for said detention, Harry could easily have kept both appointments that night; especially since Dumbledore's lesson appears to take very little time.
Plot hole: In the first potions class, Slughorn shows them a few potions and says that these are some of what the students should be able to prepare after completing their N.E.W.Ts. But later on in the book, Ron asks Harry to check his textbook to see if they can prepare a stock of it for themselves. Harry says it's very complicated and that it takes six months to stew. If that were so, how did Slughorn prepare it for their first class? He barely had even 2 months since Dumbledore hired him.
Continuity: When Harry and Dumbledore are in the second chamber in the cave it says, "The greenish glow and the light from the two wands." There should be only be one wand lit which is Dumbledore's, because it never says Harry lights his wand, and it is illegal for Harry to use magic outside of Hogwarts because he is not "of age".




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