I think a significant favor was Kvothe transitioning from underdog to hyper talented vagabound wanderer? It was foreshadowed that he was going to get there, but it seemed to have less opportunities to no brute force a solution. One of my most distinct memories of WMF was the mystery of the sick nobleman. The stakes were identifiable, there was a strong tension and the twist ending regarding the perp was a pleasant surprise in how it came from a place of concern rather than malice.
The magic and fighting and misc world building is hazier. Not saying I rage quit or nothing, I thoroughly enjoyed it in the moment but apparently, I'm a sucker for those traditional heros journey formats.
The strength of this series is something that I think is something that throws off a lot of first time readers: It's diversity.
The nature of Kvothe's adventure is that he keeps getting wrapped up in one thing or another at different times. One moment, he's just trying to pass his exams, then his rival poisons him so now he's trying to find a way to guard himself against magic, then he realized his rival stole his love's rings so then it becomes a heist, then he goes to Vint where he has to play games of political intrigue, then he's hunting bandits, then he's in a kung fu movie learning martial arts.
I agree with you that him trying to solve the mystery of the Maer's sickness was the most intriguing part of the book for me personally. But then, all of a sudden, he's on this nature trek with a dumb mercenary hunting bandits. For me, that swerve made it the only part of WMF that I disliked...but on my second reread, seeing it coming, it helped me better understand what the purpose of that section was. The way you describe it, about not being clear on what the stakes are, is actually pretty good. Every time Kvothe's adventure changes, the paradigm of the narrative shifts. The stakes from before are still important, but put on the backburner while something new is developed.
I'm of the belief that there aren't really any bad parts, but the diversity of the types of stories that Kvothe goes on means that one is going to be your favorite, so you're going to be upset when that part ends. You and me, we love the political intrigue episode, but some people hated it, while others found Adem to be their favorite part. I think I've heard each part of the series described as someone's favorite and most hated part, because how much a given thing appeals to you innately depends on what kind of reader you are.
But this is one of those books that improve on a second reading. You get a clearer picture of whats going on and why it matters and why the part you liked before had to end. And while you might not like this new adventure as much, I've gone over this series with a fine tooth comb and it mostly checks out in terms of technical standards of good writing. Every part develops Kvothe's character in some way, it builds the world, it progresses the plot, it's often really well written in temrs of prose, and so on. It's just harder to see as a first time reader because what Kvothe is doing at any given time can change at any given moment, and if you don't like it and would prefer to go back to what he was doing before, it can be harder to see that.