Harry is back to his old self, assuming Malfoy's plan is not working based on his physical appearance.

House elves show up again in Slughorn's casual reference that he has had them taste all the bottles.

We learn of Horcruxes. And the number 7.
It is very interesting that Dumbledore would say that as far as he knew no wizard had ever done more than rip his soul in two. This seems a little strange. Surely Grindewald or someone like that has killed more than two people? Of course, it does suggest the strong taboo of killing in the wizarding world. Perhaps he was just referring to the amount of horcruxes made, even if that is not what his words say.

I am a little fascinated by this (the pacifist in me, perhaps). What of the people killed in battle by the good guys? I cannot remember who kills who, but if Mrs Weasley kills Bellatrix, is her soul broken in two? Would she regret it enough to heal it again? Or when Harry kills Voldemort...

At any rate, we can start ticking off horcruxes (although if Voldemort split his soul in seven, shouldn't there be six horcruxes to begin with, then five left after he has used one of them to gain a life? Or is it a way of keeping the embodied soul suspended, so that it does not disappear when the body is killed? -- I was always a little unclear on that): the diary. One down, six to go. The ring. Two down...

So there are now four. And Voldemort.
The locket
The cup
Nagini
and Rowena Ravenclaw's tiara, if I am right?
And Harry?
Which brings us to ... 8?
I have always had trouble with this part of the books. Counting is not my strong suit, and I have a strong impression that Dumbeldore's counting is off here too. How does Harry fit in? Is he really a horcrux?

Anyway, the dicsussion in Dumbledore's office also clarifies why Draco is being punished. It is not just Lucius' failure, but his lack of care with the diary.

The discussion of prophecies is also interesting. If there are so many prophecies that do not come to pass, what is their importance? Are they the "most likely" scenario only? Are they triggered by being part of a series of events (Snape listening outside the door sets Trelawny off?) ... I am intrigued. At any rate, the power of choice is quite central again. While the presence of Prophecy had seemed to dampen it, that is here revoked.

We are also shown the hiding room version of the Room of Requirement, which will become important later. It is a little strange that he does not react to the Vanishing cabinet being there. After all, there is no reason why it should have to be hidden. Unless someone is up to no good. It is quite a well hidden clue, though. As is the tiara.

And I really enjoy Harry defending the Prince against Hermione's suggestion that he might be bad. If only he knew he was so sure Snape was not a bad guy.