Just to update this thread and correct myself. The book is absolutely fine. The problem was we were using it at bedtime with dimmed bedroom lighting. When we turn the bedroom lights back on, the book works fine again!

Is it that the reflection of the already-on LED (or maybe external light at the right angle) is hitting the sensor used for NOT and then creating a feedback loop to keep the light on when the switch isn't pressed? This happened a few times, and either changing the ambient light or holding the book tightly shut will resolve the issue on my copy.

edit: because the author is here, thanks for the book: an interesting idea and well-executed. Daughter doesn't mind the front page blue LED. I am more amused than annoyed: even a two-transistor circuit needs debugging sometimes.