The Notebook?

I wouldn't consider that to be a plot problem at all.

The movie is all about "purpose", and Hugo's purpose is to fix what's broken. In the movie it's pretty obvious that his purpose is to fix the automaton (robot) and Papa Georges, and thereby "fulfill his purpose".

Hugo needed to fix the automaton to finally be able to "let go of his father", and receive what he refers to as a "message from his father". He might have been thinking that he needed the notebook to do that, but he managed to do this without it. So, in other words, the notebook was irrelevant. Hugo got his conclusion, and didn't "feel alone anymore". It wouldn't add anything relevant to the movie if Papa Georges gave the notebook back to Hugo.

Sand is overrated. It's just tiny, little rocks.

Well, in the book it's a little clearer. As he works on the automaton, he second guesses himself, thinking whether or not he can fix it without his father help or the notebook. When he does, he finally understands his our skills and what he can do on his own. They kinda glazed over it in the movie, though.

I got so lost. I thought we were gonna have a full on Nicholas Sparks conversation in the Hugo message board. It was like loosing your virginity- mysterious, but exciting in a way