Towards the beginning of the film's prologue, Oliver is imagining what would happen if he were to die. In the daydream, Oliver refers to the man on the PA system as "Mr. Dunthorne". This is most likely a reference to Joe Dunthorne, the author of the novel which the movie is based upon.
As Oliver daydreams about people's reaction to his death, he mentions 'Mr Dunthorne' (and his quavering voice). This could be the teacher or perhaps the Headmaster. Mr (Joe) Dunthorne is also the name of the author of the book upon which the film is based.
Each of the main characters has a colour which can be seen in their clothes and possessions. Oliver is blue, Jordana is red, Jill is yellow, Lloyd is brown and Graham is black. As Oliver gets to know Jordana more and more red sneaks into his palette.
When Oliver leaves Jordana's house after Christmas dinner, the car parked in the driveway is a 1997 Vauxhall Astra. The film is set eleven years previously in 1986.
The pencil drawing of Oliver's mom initially appears with a single half way fold when she looked at it. When Oliver found it, it was folded twice. But on close up of the drawing, the folds have completely disappeared.
Towards the end of the film, when Jordana sits next to her new boyfriend while talking to Oliver, she puts her hair back behind her ears. In the very next shot, her hair is back in front of her ears.
Oliver Tate: My Dear Americans, The film you are about to see is a biopic of my life. The events take place, not so long ago, in a proud land called Wales. Wales is next to England, a country you pretend to treat as an equal. My homeland has produced Catherine Zeta-Jones, Tom Jones and some other people. You have not yet invaded my country and for this I thank you. Submarine is an important film. Watch it with respect. Fond regards from your protagonist, Oliver Tate.