Well, the third installment is where they really start elaborating on things, and dealing with bigger plots since the world has become more established and the characters are a bit older and as a result a bit more conceptually capable. One of the things about the series is that the plotlines grow up with the characters. The first couple of stories had the protagonists as little kids, and who had very limited powers, as they got older their powers were growing (as was how assertive the school/ministry was being about them using those greater powers outside of school). To begin with it was mostly about mysteries and some inevitable ex deus machine when things got real, while that still always applied to an extent, the characters who were all quite talented with magic (even Ron) were developing their offensive spells (even if they practiced in secret), and getting permission to use more powerful magical devices like the Time Tuner. The third movie did a decent job of creating a malevolent presence and then doing a role-reversal with it later, as well as having the bad guys get a little more aggressive, as the protagonist himself was beginning (like most kids) to break more rules more assertively and render himself more vulnerable, as well as cover a wider area where he couldn't be kept under close protection as regularly. Also the "Death Eaters" are supposed to be rebuilding so they become stronger as the stories go on, as opposed to being as powerful as they are in the final chapter all at once, which is why when they start making their little terror raids it's noticible to everyone.
From a movie making perspective I think the third one is one of the weakest when you consider it from the perspective of the books, but probably worked better from the sake of a straight film, especially when dealing with an audience who never read and thus were not pre-existing fans of the material. The directors for example made a big deal about being all excited about how they could get the characters out of their school robes and such and have them wear "normal clothes" for the Hogsmeade scenes (which wasn't really in keeping with the books) but actually probably helped ground the movie for the casual movie goers by making the characters seem more normal, and thus more relatable.
That said, as good as these movies were overall, I do not think they will remain the final word on the franchise as there is a lot of potential for improvement and doing things better, and more accurately, to the source material. As much as many people hate to admit it, there is a certain amount of depth to these stories even if they are children's fare, and that's part of what sold it. The movies communicate the basic points, but miss a lot of the subtext and fun little details that made the books enchant so many people even if JK Rowling isn't the best writer out there. If they could do each book as a mini-series on something like HBO where they have a decent budget, I think the results can be improved.
