Continuity mistake: When William takes Anna back to his flat, after the orange juice incident. His shirt is stained, she comes into the flat and changes. Then she leaves. When she returns to get her books, his shirt is still stained but after she kisses him the stain is gone. An impressive kiss...
Continuity mistake: After William leaves the movie set, in the next shot he goes back to the book shop. Seen through the window is the table with the books and globes. Then when Anna is standing near the window, we see that there are completely different kinds of books on the top shelf now.
Continuity mistake: In the scene where Julia Robert's character first goes to Hugh Grant's character's flat, there's a chalkboard that's telling Spike to clean up. It's quite small writing, but in a close-up of Hugh Grant when he's directing her upstairs it's clearly larger. It then goes small again until she comes downstairs, when it goes large and stays that way.