Instead of derailing another thread into whether or not the White Court would respect Harry as Lara's husband because they see him as a dumb brute, I'll deal with it here. I'll list what I think are situations in which he manipulated people into doing what he wanted in a way that the White Court might respect, then I'll list the effect it would have.
The Books:
Storm Front: I don't see anything.
Fool Moon: I don't see anything.
Grave Peril: He manipulates Lea into letting him go.
Summer Knight: I don't see anything other than Mab appreciating what Harry did in GP.
Death Masks: I don't see anything.
Blood Rites: Lara declares that Harry has "made me the cat's-paw for you, Dresden. While making me think I had the advantage of you. You've played me at my own game, and ably."
Dead Beat: Though he didn't intend any of it, he managed to get the Wardens to help him get hold of the Word of Kemmler and deliver it to Mavra. And get put on the Wardens payroll at the same time.
Proven Guilty: He bested the Merlin in Molly's trial. The Merlin had to use his brute institutional strength to beat Harry. Then Harry used a parliamentarian/procedural trick to stop the Merlin, with the help of the Gatekeeper, until enough of the Senior Council showed up to give Harry what he wanted.
This was done in front of many Council Members and the Summer Lady and Knight.
White Night: He turned a White Court scheme being run by all three major houses to his advantage. He got the paranet going, acquired a big obligation from the Little Folk, and got a big reputational boost among them as well.
Small Favor: He manipulated Nicodemus into defeat. Nicodemus had won. Dresden convinced him to risk everything he had gained, and he lost all of it.
Turn Coat: He manipulated the White Council into fighting Shagnasty. He appeared to manipulate the White Court into doing the same, but iirc, Lara was in on it. He manipulated Peabody into incriminating himself.
Changes: He dealed with Mab in a scheming manner that she respected.
Ghost Story: I don't see anything, other than Mab's confirmation of what I said for Changes.
Cold Days: He was in deep with Faeries and Outsiders and managed to see through several misdirections. (But didn't catch some based on what the Redcap said in BG).
Skin Game: He once again duped Nicodemus. He saw what Mab and Marcone were doing.
Peace Talks: He put the White Court under his thumb. He shamed Marcone because Marcone lost custody of a helpless prisoner. He manipulated a member of the Senior Council into doing his bidding. He tricked another Senior Council member into fighting a whatever you call his double on the dock.
Battle Ground: He "manipulated" a massive army of the Little Folk into fighting for him. He got the eye, denied it, and by doing so, got Marcone to give him a super warded castle. He also convinced the Accorded Members present to pay a weregild to the mortals.
Short Stories:
In B is for Bigfoot, Harry manages to achieve his goals without any direct action. He did what he was hired to do without causing any trouble with the Svartalves.
In Jury Duty, Harry's in the middle of the conflict between the White Court and Marcone.
The effect:
I'm not sure how widely known Harry's tricking of Lea in GP would be.
I don't think anyone would be able to easily piece together what Harry did in BR, so I don't think we should count that one.
From DB, I'm not sure who would know enough to draw any conclusions other than Mavra. She, at least, should understand that he isn't just a brute.
PG is the first thing he's done that people in the community are likely to know about. Faeries trade secrets all the time. Everyone in Titania's court had a big laugh about how he spent the favor from Titania. Enough of them probably got the story of how he got the favor to spread it around sufficiently for anyone who wanted information on Harry to get the story too.
From WN, everyone should know that he foiled the Skavis and Malvora plans. Whether or not they were able to piece together what he got out of Lara is less certain, but the Little Folk certainly know, and they don't guard information all that closely. I'm not sure if the White Court would be aware of the weregild paid out to Harry, but the sharper members of the Court and broader community should be able to piece it together.
I'm not sure how widely known the details of his defeat of Nicodemus in SmF would be. The White and Black Council's should know as Luccio was involved.
What he did in TC would be widely known in the Council and the White Court. Different particulars might be fuzzy in each, but they'd be known.
I don't think any but Demonreach, Bonnie, Molly, Mab, Kincaid, and Harry know that he almost out foxed Mab in Changes.
The White Court would be aware that they attacked a bunch of cultists during CD. Probably that it was at the direction of Dresden.
I don't think his exploits in PT would be widely known. Which is the point of a lot of scheming.
I think everything he did in BG will be widely known.
Harry's actions in B is for Bigfoot probably made an impression on Svartalves. They probably don't share information as freely as other elements of the supernatural world.
In Jury Duty, he foiled a White Court plan, but he was Marcone's cats-paw at the time.
Conclusion:
I think any supernatural player that wants to develop a dossier on Harry ought to be able to get enough information to figure out he isn't just a dumb brute. Fairies and members of the White Court are especially well positioned to do this. The supernaturals that think Harry is a dumb brute are pretty much going to be the ones that Harry has to worry the least about because they will be the least informed, most arrogant, and/or stupidest.
Thoughts?