Few thoughts and such, and I'm sure I'll get many things wrong as it's been a while since I've re-read any of the previous books, but who cares?
1. I was very glad that there wasn't a "Last time at Hogwarts" thing. Seems like in every book after Philosopher/Sorcerer's Stone, Harry had to re-introduce everyone and mention what they did. If I'm reading the 6th book, there's a good chance I've read the other five.
2. Why/how are the memories (Not just from the Pensieve, but also Riddle's diary), in third person? I was going to mention the thing with Snape's memory from Order of the Phoenix, but decided against it, due to this being a discussion on Half-Blood Prince.
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More later, maybe, but probably not. Good read, though.