The good; The way they deployed Alicia Keys's catalog was well done. They started with lesser known (and the handful of original) numbers so that you were invested in the story and characters before being distracted by her biggest hits.
When those big hits were deployed, they did a great job adapting them to the stage. I didn't feel like any of them were overly shoehorned into the show, and her biggest hits were all either exactly right for the moments they were used or adjusted in a way that helped the song feel dramatically integrated. Giving BVD the start of If I Ain't Got You and Fallin' were excellent choices. The tempo/style changes on Fallin' were jarring, but fixable. And using Girl on Fire and Empire State of Mind for big celebratory moments worked (extra smart to use the Alicia Keys version of ESOM instead of the Jay-Z ft. Alicia Keys version).
The overall structure of the show works. It's a fairly straightforward coming-of-age story, but it hits all of the big emotional moments that it strives for and never feels (at least to me) overly treacly or sentimental.
Room for Improvement:
I do think they're trying to do a bit too much with the book. There are a whole bunch of ensemble characters who have very small bit parts (Ali's friends, Jersey's friends, Nuck's friends....basically all of the friends) that either need further development or could just be cut.
The Nuck arrest feels the most unnecessary element. Bringing in the cop and having him be the victim of police mistreatment felt preachy and cartoonish. I understand wanting to set up Perfect Way to Die (which Kecia Lewis DESTROYS), but they could just as easily have that moment be a story from Liza Jane's past (she's old enough to have lived through the Civil Rights movement). Because currently it makes Ali's emotional response be about Nuck, and that feels forced. There's enough family drama to mine between Ali and Nuck and Jersey's overprotectiveness that the extra layer of plot on top of it brought it perilously close to melodrama.
There are a handful of clunky lyrics in the new songs, but nothing unforgivable.
The choreography and staging were interesting and compelling but also claustrophobic and confusing. Perhaps on a larger stage it will breathe better, but I could have used a slightly smaller ensemble. There are moments where the choreography really adds to the narrative (I'm forgetting the song, but the choreo during the post-Nuck-moving-to-Atlanta number was FANTASTIC!). Other times it was unclear why the dancers were there at all.
I think 95% of the book issues could be fixed with a very clear statement from Ali at the beginning of the show that the story that's about to be told is how she remembers it. The fact that she talks directly to the audience throughout the show implies that, but it could be much more clearly elucidated at the top of the show. Doing so also could lessen any scrutiny on the choppier parts of the book ("Of course it's a little messy, that's just how *she* remembers it at 17...the details aren't as important"). It's a cheat, of course, but one that could help a lot.