I thought with Slughorn it was really interesting how he talked to Harry about knowing his Father in school. I almost thought he was going to talk about James and Lily for a second, but then it became clear he meant Tom Riddle. Does he know who Harry's real parents are? Is he actually interested in him because he thinks he's Voldemort's son, or is he interested because he is Lily's son? Harry has Lily's eyes; would that be enough for people who knew Lily to figure out who he is, in the absence of other evidence?

The other student he was immediately interested in is Pansy. Is it because he saw her posts from earlier and finds her interesting? Or, more likely, because one of her parents stood out to him as being special? I'm guessing her father, but it would also be cool if it were her mother who used to be particularly brilliant and talented before circumstances drove her to alcoholism.