In the beginning of the film, Jenny's fringe is neatly parted. As she becomes more and more involved with David, her fringe starts to descend until it is completely down. This shows she is now a part of his world. Then, as she starts to move away from him, her hair becomes parted again.
Director Lone Scherfig says she experimented with giving the actors options during scenes. For instance, she told Peter Sarsgaard that if he felt like it he could start a conversation with an extra playing a doorman in one scene despite there not being any written dialogue.
In the final scene Jenny and her friend can be seen cycling into the Bodleian library courtyard. Bikes are not allowed in the Bodleian and others can be seen chained to the railings outside. There are also 3 steps up to this courtyard which they would not have been able to cycle up.
In the dog track parking lot, David takes a few things out of the back of his car and sets them on the ground. Although they are seen there throughout the scene, they are suddenly gone when he and Jenny leave even though he is never seen putting them back.