To be honest, I haven't thought this much, but I watched Notting Hill again a while ago and thought that it was a very well made movie. Especially when it came to the script. Of course the acting was good too.
Now, as many are aware, Blake Snyder's Save the Cat book series is about deconstructing movie screenplays. His books deal with the structure of the movies and teach the readers to write scripts themselves.
Anyway, in his books there's this concept of 'saving the cat', which basically says that the audience needs to have a reason to root for the main character(s). There has to be something in the script that makes us interested in them.
It sounds simple, and it kinda is too, but you wouldn't believe how many movies manage to screw it up. Too many times the writers simply didn't get it.
Notting Hill on the other hand does it probably better than any other movie.
What makes this scene so great is that not only does it put Hugh Grant's main character into a tough and an awkward spot, but the way he sorts it out tells the audience that he's a really good person.
I don't know about you, but if I were Julia Roberts' character in that situation, I would be impressed as hell. Maybe it wouldn't make me fall in love with the person in question immediately..
..but it certainly would make me feel good about life - which is exactly what great writing is all about.