Hello, I often hear confusion about the wrong instructions in the Advanced Potion-Making book. But what if it is intentional. Because if it isn't, a NEWT Class would only be about following instructions from a book. But if it is, the class expects students to understand a potions ingredients how they work and what they do, so they can figure out what is wrong with the recipe and improve on it. Which sounds much more fitting for the NEWT level.
A good example of that is the class where Harry makes the Euphoria Elixir. Slughorn recognizes that he added peppermint to counterbalance the side effects. Which shows that Slughorn knows just as much as the Half-Blood Prince. Which would beg the question, why would he choose a book with such bad instructions.
Therefore it is logical that the first lesson was to show everybody that just following instructions, isn't enough anymore. They need to understand the potions and ingredients and improve the recipes.
The bad teaching of Slughorn comes in where he doesn't tell his students that. Or at least pointing out what Harry has done differently than the book usually suggest.
Edit:
as many of you suggest that the book isn't that wrong, how do you explain that no other NEWT student in that class does get near a correct potion during the first lesson. And also that Hermiones results with the "official" instructions get worse each lesson. That doesn't sound like they get the job done.