The characters differ a great deal from the original, the movies and even the version my mom used to share before bedtime where Kate waved a rifle around and so on so at first I felt a tad cheated in my expectations. Although the new versions are easier to laugh at, the new version shakes off one of the main elements of continuity, beside the title.
I am unsure of the target public as both Kate and Petruchio feel a little child-like and simple because of their energy and joyfullness, attitude which sits quite at odds with the kiss, "remove an article of clothing of your choice" gambit or Gabrielle's vocabulary. The child-like temperament then changes a lot in a very short time. Apart from that Petruchio alternately calls Kate by the nickname or 'madam' which differ greatly in formality, especially for that time.
About the first Lucentio/Biance scene, it was either reavealing as to Lucentio's previously nonexistent dark character streak or hilarious in the way that an overy angered child throws a tantrum. Either way, I believe new Lucentio went from originally wimpish to downright stupid.
When Kate arrives, neither she nor Petruchio show none of the salt-in-the-wound temperament that made them both so famous and for the first time Bianca becomes the focal point of the whole stage.
At this point, I finished the first fifth of the book and I sincerely believe that it bears none but the smallest resemblance - title and names - to Shakespeare's initial work. It's too late to revert the characters back without seriously exaggerating.
As a stand-alone this book alternates between childishly funny and soap-opera dramatic, a very unfortunate mix, indeed.