I really enjoyed the episode. Is it cheesy? Yes, but that's part of why I like it. :'D The whole stuff with "Fly High", the balloon or the coat all probably fall into that category but I like that, it warms my heart. I absolutely loved the teacher!
They obviously changed the New York/vocal lessons thing (with ayu actually attending properly, the marathon) but I feel like they did a good job using it as a way to show ayu's strength & will power. She often thought about giving up but knew she had to keep going.
Only thing I'm not entirely sold on is Reika (the secretary). In itself, her role is a fitting concept but lines like "I can see her dark future" or the 'be my right eye' are kinda out of place.
Judged by the concert scene, they are giving very clear nods to some of her iconic looks but it doesn't seem like they actually try to re-create any specific performance. It's more for the sake of evoking a feeling of nostalgia within people.
The drama isn't perfect but personally, I'm very happy with the outcome so far.