When Annie is teaching Sam when to feed Lucy and they are talking about what "Lucy in the Sky with Diamonds" is about, Annie says "But John Lennon said, it was about a friend of his son Julian Lennon's from school - Lucy O'Connell". The real girl's name was "Lucy O'Donnell".
In the very beginning shot, when Sam is sorting sugar packets in the holders, he puts the brown "raw sugar" packets in front. When he is shown setting the holders on the tables, the brown packets are in the middle.
When Sam and Lucy are being observed and they are talking, just before Lucy talks to the people observing her she turns her head towards the "camera". The next shot, she turns her head again before talking.