I love the fact that Harry improves in his preparedness and knowledge as the books go on. Lots of characters in fiction pick up new gadgets/powers/asspulls to deal with various problems but Harry shows genuine growth from book to book that directly follows behind him having a bad time and then taking that lesson to heart. For example, when he took up running after realizing that he sucked at escaping on foot or creating the to-go bag of his kit for emergency situations. It also says a lot that he makes improvements on his own while his circle of friends are already specialists in one way or another and not always available to be a skeleton key for him. I also love the fact that information doesn't go to waste. Changes in the world and events that have happened come back and play a part even if only to add color to certain situations.

As for spoiler-y stuff I've noticed he's had recurring headaches for a few books now and I'm wondering if that's gonna lead to something. They were more intense in Small Favor but I think I remember them cropping up in White Night