The biggest mistake, I think, was the unnecessarily adversarial relationship between Murphy and Harry, up to halfway through Summer Knight. Murphy's an antagonist for the first few books, and I think it hurt, rather than helped, the story. Thankfully, Jim realized that it was getting old and nixed that conflict with in-universe justification; we actually got to see that shake out on the page, for which I'm grateful. (Too many other authors would just have the character change between books and add a line of dialogue to say, "Yeah, well, I trust you now because of some reasons I have.")
The other thing that was dated, and looks like is now gone: the Two Lines, No Waiting aspect of the early books. Harry's constantly jumping back and forth between cases (until, inevitably, they're revealed to be intimately related) for several books. I think that's gone for the most part, at least since Turn Coat, and I'm happy about it. It lets Jim write more focused, tighter, and effective stories when he's not juggling as much.
I don't think they were necessarily a mistake; they worked okay, but, for example, Skin Game is a much more fluid narrative by comparison.
In terms of the rules of how the Dresden Files Universe operates: honestly, not much I can point to that's particularly inconsistent. Magic A is Magic A, and that's been the case from Storm Front. Jim very clearly sat down and figured out what magic was, how it worked, and what Harry could do with it, and he did that before he wrote a word. The Laws of Magic have indeed shifted (much like what a Steadholder was from Furies of Calderon to Academ's Fury), but they're pretty consistent after Summer Knight.
I can't think of any examples where magic did something it shouldn't have been able to, but maybe my old brain is leaking again. The closest is Bob refusing to listen to Harry in Storm Front, despite Harry having ownership of his Skull. Harry rips up some of his desperately needed cash because Bob was being ornery.
Miscellaneous Others:
1. Harry constantly being broke. That got real old, real fast, at least for me. I'm not saying he should've been rolling in it, but a big chunk of the first several books deals with Harry trying to figure out how to pay his freaking rent. This stopped being an issue from Proven Guilty on, thankfully. I get the purpose; Harry lacked resources, and that made him less effective. But...c'mon.
2. Susan. I didn't like her from the start, and didn't start to like her after she was half-turned. I felt nothing when she died, except a bit of sympathy for Harry—but again, that's not sympathy for Susan. To me, if you show up to a vampire party, you should expect to be eaten. I didn't get their relationship, and I think Jim realized some of that (along with his "Lois Lane" remark about her character). I think if the books had focused more on her character and what she was up to, what she wanted, and her motivation for doing the things she did, I'd probably feel differently. But that would've dragged down the story in other ways, so meh.
I'm really scraping the bottom of the barrel in terms of criticism, here. There is very little that I can point to in the series as bad. Even the writing for the first few books is, you know, fine, if a bit inexperienced (the best way I can describe Storm Front is that it very much reads like an author's first book). The worst I can say about Storm Front/Fool Moon/Grave Peril is that each scene was essentially, "I went to a place, and a thing happened. I left that place." But he moved past that quickly. And pretty much all of my petty little gripes were "fixed" (from my perspective; others will very likely disagree with me).
