The Danish title 'Hævnen' translates into English as 'Revenge'. Susanne Bier mentioned that she prefers the English title 'In a Better World' which emphasizes the hopefulness of the film while the Danish title emphasizes the severeness of the film (at 1:52:49 in the Blu-ray director's commentary).
At 13:37 in the Blu-ray director's commentary, Susanne Bier notes that Elias' braces were Markus Rygaard's own braces, not filming props. Having the bullies call him "rat face" was devised after casting, reasoning that, were he bullied, it would be in part for the braces.
In the first minutes of the movie, the white T-Shirt that Anton (Mikael Persbrandt) is wearing during the surgery of the little girl gets blood stained (at around 24 mins). When finished and outside the tent, the stain is much smaller and misplaced (at around 20 mins). When leaving on the small truck, the blood stain has moved once more (at around 50 mins).
When Anton (Michael Persbrant) performs his first surgery he scratches his head/corrects the position of his mask after having put on sterile gloves (at around 42 mins) thereby contaminating them and risking that the patient gets infected. A real surgeon would never do this, and if she or he did, she or he would change gloves.