I read the book a while ago but I don't remember anything about Madeleine having an affair or the whole puppet show storyline, did that happen?
Also, I could have sworn it was Jane who pushed Perry to his death (off a balcony, as it was in the book) and I thought that was something else that was changed in the series until I started reading this thread.
One thing I didn't think worked as well in the series was Perry using a different name; in the book he uses his cousin's name so when Madeline Googles him and tells Celeste there's this whole storyline going for a bit about it possibly being Perry's cousin and how Celeste is going to prove it was him/confront Perry about him,etc - don't think it worked as well in the series in fact the false name wasn't even explained. I also think it made it so much more obvious that it was Perry.
I do think that it was much more of a whodunnit than the book which meant a lot of setting up of red herrings that meant plot lines that never happened in the book(Ed and Madelines ex constantly about to fight, Madelines affair,etc) but I guess that was necessary.
Also, didn't see Jane end up with nice not-gay barista, unlike the book, which I thought was a shame.
All that said, I loved it 