Throw It In: The lady's bathroom scene was improv on the part of Reese Witherspoon... except the bit where she leans into the mirror and says "Has that been on my teeth the whole time?" They had filmed an eating scene earlier in the day, and she had a piece of schmutz stuck in one of her front teeth, and her reaction to seeing it was real. They used it in the film anyway.
What Could Have Been: the original script (written in 1997) was a mix of romantic comedy and a High Concept disaster movie and featured every single monument in New York City getting destroyed. Not surprisingly, almost none of that draft made the final film.