In the inauguration party of Rosie's hotel, we see Ruby in frame. After 13 seconds, we see Ruby running though the front door which is not possible.
When Rosie is applying to college, she applies to Boston College and yet receives an acceptance letter from Boston University, a totally different college.
Alex leaves for the United States to go to Harvard for medical school, but he only just graduated from high school at 18 years old. Unlike in the United Kingdom, medical schools in the United States require a bachelor's degree for admission.
Many of the cars throughout the movie were not yet produced in the year it was meant to be.
Both the Fiat Punto parked near Rosie's house and the Mercedes at the hotel have the same VX02... number plate (possibly identical) despite it being pre 2002.
When Rosie leaves the car with Greg for college dance, we can listen that the audio of Alex saying "Wanker!" precedes the video.
When Alex takes Rosie to his Boston apartment for dinner, his "American" girlfriend (played by English actress Tamsin Egerton) explains the menu for the evening. She states that the entrée is finished with rocket sauce. Rocket is the British term. An American like Sally would call it arugula.
Sally and Alex have cake with white wine while it's dark outsides. Then Alex exchanges text messages with Rosie who's on the beach during daytime. Either Rosie is on the beach very early and Sally and Alex had a very late dinner - or Sally and Alex are having wine and cake for breakfast - or someone ignored that Boston is 5 hours behind the UK, not ahead of it.