After having some time to reflect, I think I've decided that the newest Harry Potter book is not necessarily the best one since the first, but it is definitely better than the last and a very worthy addition to the series.
Why is Harry Potter so popular among adults? So ask various adults in the blogosphere and elsewhere, some of whom have even tried reading one or two of the books but don't get what the fuss is about. I'm not sure how much genuine interest there is in understanding the matter, but, to take the question seriously, I think one has to break the matter into understanding (a) why the first books came to be popular and (b) why the latter books continue to be as (or even more) popular. The answer to the latter is simpler, I think, insofar as once you get to read people to read three books in a series for which there is an ongoing storyline, it's a lot easier to get them to read the rest, regardless of age. Even so, I think Rowling was very smart in making plain from the outset that this was going to be a seven-book series, so that people feel they really are following a genuine dramatic arc that will culminate, as opposed to some open-ended series where either it feels like there is no end or each book is written like it might, or might not, be the last.
As for why the first books are popular, I have to admit to some annoyance when people say that the Harry Potter books are just a swirling knocking of A, B, C, D, and E, where the cited sources vary but are usually a hodgepodge of boys adventure stories. If you want to understand why the first three Harry Potter books are popular among adults, I think you have to appreciate that, while they have adventure story elements, they are really more mystery stories. I mean, however much Rowling might lift from whoever, whoever, whoever, whoever, she also develops a interesting little whodunit and adapts various classic devices from the suspense-mystery format to the world of the books.
Wherever she draws her inspiration from, the first books also draw a world with all kinds of clever little touches and continually imbued with this sense of wonder and fun. Frankly, compared with certain other writers in the children's/young-adult fantasy genre, part of the appeal of the Potter books is that it's full of cleverness but doesn't start taking its world too seriously--you don't get the image of some creepy male author sitting in an attic typing out page after page of the fantasy world that he had first started conjuring as an adolescent as a way of coping with what a pimply loner freakazoid he was.
More precisely, I think, the appeal of the series to adults is really to be explained most importantly by the first book, which starts out with this cute and uplifting story about a downtrodden boy getting introduced to this fascinating new world but then, before you quite realize what has happened, turns also into this compelling little page-turner with an ending clever enough that you feel gratified by it even though you are an adult. The second and third books were good follow-ups in the sense of providing both creative enough elaborations on the world she had created and, again, a suspense/mystery plotline that was engaging enough to keep you reading and then which had an ending Clever Enough For Adults.
After that, I mean, this is why all careerist mystery novels try to start series: once you get readers hooked into a series, you've got it made.
As far as their character as mystery novels goes, I think Rowling is helped greatly in hoodwinking her adult readers by their knowing that they are reading a book whose primary audience is children. When I'm reading an adult mystery novel, I have a pretty good sense of calibration for clues and plot twists and whatever--along the lines of thinking that while it would not be entirely obvious that X is the culprit, it would still be a little bit too obvious, so instead it must be Y. With several of the Harry Potter books now, I have thought that I could see ahead to how the ending was going to turn out--that would be clever enough for an eleven-year-old reader--only to realize that I had been fooled, and in a way where, indeed, in retrospect the clues did stack up nicely toward her solution.*
* FOOTNOTED SPOILER! In the most recent book, notice how she sets up the question of "Who is the half-blood prince?" and then also has there be a long series of discussions of a primary character who is a half-blood--although that phrase is not explicitly used--and seemingly just the sort of person who would be scribbling down sinister turns on spells in a textbook. Too obvious, right? But, never anywhere do any of the characters ever suspect that this character might be the Half-Blood Prince. If not in a children's book, I think I still would have thought it too obvious. Instead, though, I took for granted that this is who the HBP would turn out to be, as a plot twist that was Good Enough For The Kids. And, lo, I was fooled. In this case, however, it was too bad that the revelation of the HBP doesn't really have much import for the rest of the story.