Foreshadowing / Harry Potter and the Half-Blood Prince

• Early on, when Dumbledore chews the Dursleys out for their treatment of Harry, he mentions that the only good thing they did was not abuse him in the same way they did Dudley. Harry notes that Dudley has a look on his face like he's trying to think of a single time he has ever been abused. By the next book, he's apparently figured it out, as he manages to have a quiet reconciliation with Harry.
• During her and her sister's visit to Snape, Bellatrix mentions this line, "The Dark Lord has, in the past, entrusted me with his most precious —". In Book 7, it is deduced by Harry that Bellatrix was entrusted with one of Voldemort's Horcruxes, though Bellatrix was not fully aware of the relic's value at the time.
• Snape is treating Pettigrew very badly in this book, even when counting Rewarded as a Traitor Deserves. Book 7 reveals Snape was in love with Lily, who Voldemort killed after Pettigrew ratted on her and James.
• While talking with Slughorn to persuade him to come out of retirement, there's a moment where Harry and Slughorn notice the ring Dumbledore is wearing on his finger. Slughorn is specifically mentioned to be frowning. He recognizes the ring — it was worn by Tom Riddle. Including in the memory of him asking Slughorn about Horcruxes.
• The first Potions lesson, Slughorn points out several cauldrons full of various potions he has prepared. Each of them ends up playing a role in this book. The Felix Felicis gives Harry the right circumstances to get a memory and keeps the gang safe from most spells during the battle; the Amorentia is a love potion, which Ron ends up accidentally ingesting, and likely the potion Merope used to get Tom Riddle to fall in love with her; and the Polyjuice Potion is how Malfoy got his hands on the supply to use on Crabbe and Goyle.
• When Harry smells the love potion, he smells a few things, including "a flowery scent he couldn't identify, but which reminded him of the Burrow." Slughorn says everyone smells something different, based on what attracts them. Harry later notices the same flowery scent from Ginny, but doesn't make the connection.
• Harry notices that the barman from the Hog's Head was putting something away, after finishing up a transaction with Mudungus Fletcher. That was the other half of the two-way mirror Sirius had given Harry the year before, and what enabled Aberforth to keep an eye on Harry over the course of Book 7. Also explains the familiar eye of Dumbledore Harry saw in his own mirror's shard.
  • Speaking of said barman, when Dumbledore shows Harry his memory of the time Voldemort came to apply to work at Hogwarts and learns Dumbledore knows his underlings' identities, he tells Dumbledore that he is "omniscient as ever" and Dumbledore replies that he is "merely friends with the local barman." Assuming we're talking about the same person, they were more than just friends, as we learn in the next book.
• At the library, Hermione informs Harry that the school's Secrecy Sensors aren't able to notice specific potion bottles, as well as the fact that Filch can't tell one potion from another. The two then abruptly stop talking, as they both had just heard somebody move close behind them amongst the dark bookshelves, only to be interrupted by Madam Pince. That certain somebody was Draco, and he was eavesdropping on their conversation, which gave him the idea to send a poison to Dumbledore. Draco later admits it himself when confronting Dumbledore at the tower.
• Snape knows exactly where Harry learned the Sectumsempra spell from. Not only because of his Legilimency, but also because Snape invented the spell himself. In Book 7, Lupin even says that Sectumsempra was kind of a signature spell for Snape.
• The revelation that Madame Rosmerta was Imperiused for most of the book had hints here and there, eventually mentioned by Dumbledore later. When Hermione thinks Rosmerta is in the back and getting more Firewhiskey, she's actually in the bathroom and waiting to hand the package with the cursed necklace to a Hogwarts student. And Slughorn mentions the mead he was meant to give Dumbledore for Christmas was from Rosmerta.
• "Severus... I need Severus." Dumbledore realized his death was near, whether by a Death Eater's hand or the curse he's suffering from, and was trying to make sure his plan could still be pulled off.
• "Severus... please..." Dumbledore is not begging to be spared here.
• While attending Dumbledore's funeral, Harry notices that Rita Skeeter is one of the attendees, and he's infuriated to see a notepad and quill in her hands as if to take notes. The next book reveals that she has made a highly disparaging biography of Albus Dumbledore, which uncovers plenty of shameful secrets of Albus's past that creates quite an insinuating blow to Harry's view of him for quite a while when he first finds out.

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