To get back to the OP, we might think of some relatively new questions, but such issues will probably not have much meat on the bone. In other words, they will probably be issues or ideas which have very little written in the books to go on.
For example, I've thought about Harry at the beginning of Skin Game, where he states that he has been thinking about his life, but what I mostly got out of that soliloquy was that Harry wondered who he could trust. I imagine that was partly due to Nemesis; Harry can't risk openly discussing it with any of his friends, and partly due to neither Mab nor Molly answering his calls, but we later learn that Harry also felt he wasn't being visited very often by his friends.
However, I would really like to know if Harry thought about anything else besides that. I mean he had an entire year on the island. He couldn't have spent the entire time learning how the island functioned and doing Parkour. To get more specific, at the end of Cold Days Mab told Harry that the athame Lea received from Bianca was tainted and the infection spread from Lea to Meave. In Ghost Story Lea told Harry's shade the reason she went gonzo on the Red Court was she owed them payback for the treacherous gift (meaning the athame) Bianca gave her. Has Harry thought about this at all? He knows or should remember that there were two powerful wizards (necromancers specifically) who were pretending to be Bianca's flunkies, dutifully retrieving and presenting Bianca's gifts. Cowl and Kumori didn't contest this observation when Harry told them he recognized them from Bianca's party. Cowl even played some one-upmanship on Harry by telling him that many things of consequence happened at that party that Harry wasn't aware of.
So we know Harry couldn't do any investigating while he was stuck on Demonreach, so there wasn't anything he could do concretely, but I hope in a future book this comes up, and hopefully it doesn't hit Harry out of the blue. He's smart enough to have put the pieces together. He should even be wondering how much his knowledge is worth. I mean Lea would certainly be interested that other people besides Bianca were involved in giving her the tainted athame, and Harry knows that at least one of them (Cowl) is still alive. Perhaps Mab would like some payback as well against a wizard or wizards who were instrumental in Maeves nemfection. Without their specific identities Harry might not have enough information to make a deal, but he's an investigator, it's kind-of what he does. So Harry should have thought about this topic and perhaps others while he was stuck on Demonreach Island.
So we can talk about this and other things Harry might have mulled over, but I'm not sure there will be much textural evidence to backup any ideas we might come up with.
